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Journal articles on the topic 'Random circle'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Downarowicz, Tomasz, R. Daniel Mauldin, and Tony T. Warnock. "Random circle homeomorphisms." Ergodic Theory and Dynamical Systems 12, no. 3 (1992): 441–58. http://dx.doi.org/10.1017/s014338570000688x.

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AbstractWe investigate the behaviour of random homeomorphisms of the circle induced by composing a random homeomorphism of the interval with a randomly chosen rotation. These maps and their iterates are a.s. singular and for each rational number r in [0,1) it is shown that there is a positive probability of obtaining a map with rotation number r. For a ‘canonical’ method of producing these maps, bounds on the probability of obtaining a fixed point are obtained. We estimate this probability via computer simulations in three different ways. Simulations are also carried out for two periods. It re

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2

Aldous, David. "Triangulating the Circle, at Random." American Mathematical Monthly 101, no. 3 (1994): 223. http://dx.doi.org/10.2307/2975599.

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3

Curien, Nicolas. "Dissecting the circle, at random." ESAIM: Proceedings 44 (January 2014): 129–39. http://dx.doi.org/10.1051/proc/201444007.

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4

Aldous, David. "Triangulating the Circle, at Random." American Mathematical Monthly 101, no. 3 (1994): 223–33. http://dx.doi.org/10.1080/00029890.1994.11996934.

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5

Andres, Jan. "Coexistence of Random Subharmonic Solutions of Random Impulsive Differential Equations and Inclusions on a Circle." International Journal of Bifurcation and Chaos 30, no. 10 (2020): 2050152. http://dx.doi.org/10.1142/s0218127420501527.

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The coexistence of random periodic solutions with various periods (i.e. subharmonics) is proved to random differential equations on a circle with random impulses of all integer orders. One of the theorems is also extended to random differential inclusions on a circle with multivalued deterministic impulses. These results can be roughly characterized as a further application of the randomized Sharkovsky type theorems to random impulsive differential equations and inclusions on a circle.

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6

De Gregorio, Alessandro, and Francesco Iafrate. "Telegraph random evolutions on a circle." Stochastic Processes and their Applications 141 (November 2021): 79–108. http://dx.doi.org/10.1016/j.spa.2021.07.001.

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7

Huffer, Fred W. "Some results concerning random arcs on the circle." Journal of Applied Probability 25, no. 4 (1988): 833–38. http://dx.doi.org/10.2307/3214306.

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Random arcs having random sizes are placed on a circle. Let V be the length of the uncovered portion of the circle and G be the number of uncovered gaps on the circle. Results are presented concerning the joint moments of V and G and the conditional distribution of V given G.

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8

Huffer, Fred W. "Some results concerning random arcs on the circle." Journal of Applied Probability 25, no. 04 (1988): 833–38. http://dx.doi.org/10.1017/s0021900200041644.

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Random arcs having random sizes are placed on a circle. Let V be the length of the uncovered portion of the circle and G be the number of uncovered gaps on the circle. Results are presented concerning the joint moments of V and G and the conditional distribution of V given G.

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9

Cao, Jianan, Yue Gao, and Chuanyang Wang. "A Novel Four-Step Algorithm for Detecting a Single Circle in Complex Images." Sensors 23, no. 22 (2023): 9030. http://dx.doi.org/10.3390/s23229030.

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Single-circle detection is vital in industrial automation, intelligent navigation, and structural health monitoring. In these fields, the circle is usually present in images with complex textures, multiple contours, and mass noise. However, commonly used circle-detection methods, including random sample consensus, random Hough transform, and the least squares method, lead to low detection accuracy, low efficiency, and poor stability in circle detection. To improve the accuracy, efficiency, and stability of circle detection, this paper proposes a single-circle detection algorithm by combining C

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10

Chepizhko, Oleksandr, and Thomas Franosch. "Random motion of a circle microswimmer in a random environment." New Journal of Physics 22, no. 7 (2020): 073022. http://dx.doi.org/10.1088/1367-2630/ab9708.

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11

INUI, NORIO, YOSHINAO KONISHI, NORIO KONNO, and TAKAHIRO SOSHI. "FLUCTUATIONS OF QUANTUM RANDOM WALKS ON CIRCLES." International Journal of Quantum Information 03, no. 03 (2005): 535–49. http://dx.doi.org/10.1142/s0219749905001079.

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Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and classical random walks. An analytical expression of the temporal standard deviation on a circle with odd sites is shown and its asymptotic behavior is considered for large system size. In contrast with classical random walks, the temporal fluctuation of quantum random walks depends on the position and initial conditions, since temporal standard deviation of the

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12

Staskevičiūtė, Simona. "Distributions on the circle group." Nonlinear Analysis: Modelling and Control 24, no. 3 (2019): 433–46. http://dx.doi.org/10.15388/na.2019.3.7.

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In this paper, we extend the definition of a random angle and the definition of a probability distribution of a random angle. We expand P. Lévy’s researches related to wrapping the probability distributions defined on R. We determine a relation between quasi-lattice probability distributions on R and lattice probability distributions on the unit circle S. We use the Bergström identity for comparison of a convolution of probability distributions of random angles. We also prove an inverse formula for lattice probability distributions on S.

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13

Homburg, Ale, and Hicham Zmarrou. "Dynamics and bifurcations of random circle diffeomorphism." Discrete and Continuous Dynamical Systems - Series B 10, no. 2/3, September (2008): 719–31. http://dx.doi.org/10.3934/dcdsb.2008.10.719.

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14

Gelfert, Katrin, and Örjan Stenflo. "Random iterations of homeomorphisms on the circle." Modern Stochastics: Theory and Applications 4, no. 3 (2017): 253–71. http://dx.doi.org/10.15559/17-vmsta86.

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15

Jinghu Yu. "Covering the Circle with Random Open Sets." Real Analysis Exchange 29, no. 1 (2004): 341. http://dx.doi.org/10.14321/realanalexch.29.1.0341.

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16

Specht, Eckard. "A precise algorithm to detect voids in polydisperse circle packings." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2182 (2015): 20150421. http://dx.doi.org/10.1098/rspa.2015.0421.

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Computer simulations are the primary tool for studying polydisperse particle packings quanti- tatively. For the problem of packing N unequal circles in a larger container circle, nothing is known a priori about the optimal packing (i.e. the packing with the highest packing fraction). Simulations usually start from a random initial configuration with the aim to finish with a dense final packing. Unfortunately, smaller circles often get stuck in trapped positions and prevent the rest of the packing from growing larger. Hence, the knowledge of the structure of unoccupied areas or holes inside a p

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17

Itoh, Yoshiaki, Hiroshi Maehara, and Norihide Tokushige. "Oriented graphs generated by random points on a circle." Journal of Applied Probability 37, no. 2 (2000): 534–39. http://dx.doi.org/10.1239/jap/1014842556.

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Extending the cascade model for food webs, we introduce a cyclic cascade model which is a random generation model of cyclic dominance relations. Put n species as n points Q1,Q2,…, Qn on a circle. If the counterclockwise way from Qi to Qj on the circle is shorter than the clockwise way, we say Qi dominates Qj. Consider a tournament whose dominance relations are generated from the points on a circle by this rule. We show that when we take n mutually independently distributed points on the circle, the probability of getting a regular tournament of order 2r+1 as the largest regular tournament is e

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18

Yershov, V. N., and A. A. Nemiro. "An Autocollimation Circle Reading System for the Infrared Meridian Instrument." Symposium - International Astronomical Union 166 (1995): 361. http://dx.doi.org/10.1017/s0074180900228441.

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A new autocollimation circle reading system is proposed for the reflector meridian circle (Nemiro and Streletsky, 1988). The instrument will be used for observations in the K-infrared waveband. Instead of the divided circle fixed to the instrument tube the new system has small spherical mirrors polished at the lateral surfaces of the primary mirror. The primary mirror is made from sitall and has an autocollimation system aimed at monitoring its optical axis position. The small spherical mirrors of the circle reading system link the circle readings with the primary's optical axis. The divided c

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19

Itoh, Yoshiaki, Hiroshi Maehara, and Norihide Tokushige. "Oriented graphs generated by random points on a circle." Journal of Applied Probability 37, no. 02 (2000): 534–39. http://dx.doi.org/10.1017/s0021900200015710.

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Extending the cascade model for food webs, we introduce a cyclic cascade model which is a random generation model of cyclic dominance relations. Put n species as n points Q 1,Q 2,…, Q n on a circle. If the counterclockwise way from Q i to Q j on the circle is shorter than the clockwise way, we say Q i dominates Q j . Consider a tournament whose dominance relations are generated from the points on a circle by this rule. We show that when we take n mutually independently distributed points on the circle, the probability of getting a regular tournament of order 2r+1 as the largest regular tournam

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20

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 4 (1993): 780–89. http://dx.doi.org/10.2307/3214512.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

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21

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 04 (1993): 780–89. http://dx.doi.org/10.1017/s0021900200044569.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

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22

Montero, Miquel. "Random Walks with Invariant Loop Probabilities: Stereographic Random Walks." Entropy 23, no. 6 (2021): 729. http://dx.doi.org/10.3390/e23060729.

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Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.

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23

Henze, Norbert. "On the moments of vacancy of random arcs on the circle." Journal of Applied Probability 23, no. 3 (1986): 837–40. http://dx.doi.org/10.2307/3214022.

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24

Henze, Norbert. "On the moments of vacancy of random arcs on the circle." Journal of Applied Probability 23, no. 03 (1986): 837–40. http://dx.doi.org/10.1017/s0021900200111994.

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25

Waluyo, Elsa Meriani, Arif Muchyidin, and Hadi Kusmanto. "Analysis of Students Misconception in Completing Mathematical Questions Using Certainty of Response Index (CRI)." Tadris: Jurnal Keguruan dan Ilmu Tarbiyah 4, no. 1 (2019): 27–39. http://dx.doi.org/10.24042/tadris.v4i1.2988.

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The misconception is a notion of an understanding that is inconsistent with a scientific notion or an interpretation of the relationship of unacceptable concepts. This study conducted to identify the misconception of students of class VIII MTs Negeri 9 Cirebon on the concept of a tangent circle. The research method used is a mixed method. Sampling using random sampling, so that obtained 48 student samples. The instruments used in this study were multiple choice objective tests accompanied by Certainty of Response Index (CRI) method and diagnosis interview. Based on its completeness, the analys

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26

Imany-Nabiyyi, Ramin. "The sizes of components in random circle graphs." Discussiones Mathematicae Graph Theory 28, no. 3 (2008): 511. http://dx.doi.org/10.7151/dmgt.1424.

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27

Шенгур, Светлана Виталиевна. "Statistical processing of very small random circle samples." Technology audit and production reserves 1, no. 4(15) (2014): 33. http://dx.doi.org/10.15587/2312-8372.2014.21700.

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28

Krasheninnikov, V. R., Yu E. Kuvayskova, and A. U. Subbotin. "Autoregressive models of random fields on the circle." Journal of Physics: Conference Series 1368 (November 2019): 032004. http://dx.doi.org/10.1088/1742-6596/1368/3/032004.

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29

DUBEJKO, TOMASZ. "Recurrent random walks, Liouville's theorem and circle packings." Mathematical Proceedings of the Cambridge Philosophical Society 121, no. 3 (1997): 531–46. http://dx.doi.org/10.1017/s0305004196001557.

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30

Dinwoodie, I. H. "Occupation measure for random walk on the circle." Journal of Theoretical Probability 8, no. 3 (1995): 669–77. http://dx.doi.org/10.1007/bf02218049.

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31

Angel, Omer, Tom Hutchcroft, Asaf Nachmias, and Gourab Ray. "Unimodular hyperbolic triangulations: circle packing and random walk." Inventiones mathematicae 206, no. 1 (2016): 229–68. http://dx.doi.org/10.1007/s00222-016-0653-9.

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32

Tang, JunMin. "Random coverings of the circle with i.i.d. centers." Science China Mathematics 55, no. 6 (2011): 1257–68. http://dx.doi.org/10.1007/s11425-011-4338-y.

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33

Shyu, Shyong Jian, and Kun Chen. "Visual Multiple-Secret Sharing by Circle Random Grids." SIAM Journal on Imaging Sciences 3, no. 4 (2010): 926–53. http://dx.doi.org/10.1137/080722023.

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34

Janson, Svante. "Random coverings of the circle by arcs with restricted endpoints." Journal of Applied Probability 25, no. 1 (1988): 215–19. http://dx.doi.org/10.2307/3214248.

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A circle is covered by random arcs with a given length a and endpoints chosen (independently and uniformly) among m equispaced points on the circle. The asymptotic distribution as a → 0 and m → ∞of the number of arcs required for complete coverage is given. The result connects earlier results for the cases ma = 1 (a discrete problem) and m = ∞ (the continuous limiting case).

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35

Janson, Svante. "Random coverings of the circle by arcs with restricted endpoints." Journal of Applied Probability 25, no. 01 (1988): 215–19. http://dx.doi.org/10.1017/s002190020004078x.

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A circle is covered by random arcs with a given length a and endpoints chosen (independently and uniformly) among m equispaced points on the circle. The asymptotic distribution as a → 0 and m → ∞of the number of arcs required for complete coverage is given. The result connects earlier results for the cases ma = 1 (a discrete problem) and m = ∞ (the continuous limiting case).

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36

Cawley, P., and L. G. Rigner. "Rapid Measurement of Modal Properties Using FFT Analyzers With Random Excitation." Journal of Vibration and Acoustics 108, no. 4 (1986): 394–98. http://dx.doi.org/10.1115/1.3269361.

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The use of a Nyquist plot of the H2 (Syy/Sxy*) frequency response function estimates produced by an FFT based spectrum analyzer with random excitation to obtain modal amplitudes and hence modal constants has been investigated. It has been proved that, irrespective of the frequency resolution used, the H2 estimates always lie on the true modal circle so even at coarse frequency resolution, a circle fitted to these points gives accurate values of modal amplitude. The conventional H1 (Sxy/Sxx) estimates lie inside the true modal circle. Use of the H2 technique results in major savings in the test

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37

Huillet, Thierry. "Random covering of the circle: the size of the connected components." Advances in Applied Probability 35, no. 3 (2003): 563–82. http://dx.doi.org/10.1239/aap/1059486818.

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Consider a circle of circumference 1. Throw n points at random onto this circle and append to each of these points a clockwise arc of length s. The resulting random set is a union of a random number of connected components, each with specific size. Using tools designed by Steutel, we compute the joint distribution of the lengths of the connected components. Asymptotic results are presented when n goes to ∞ and s to 0 jointly according to different regimes.

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38

Huillet, Thierry. "Random covering of the circle: the size of the connected components." Advances in Applied Probability 35, no. 03 (2003): 563–82. http://dx.doi.org/10.1017/s000186780001243x.

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Consider a circle of circumference 1. Throw n points at random onto this circle and append to each of these points a clockwise arc of length s. The resulting random set is a union of a random number of connected components, each with specific size. Using tools designed by Steutel, we compute the joint distribution of the lengths of the connected components. Asymptotic results are presented when n goes to ∞ and s to 0 jointly according to different regimes.

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39

Taff, L. G., J. E. Morrison, and R. L. Smart. "Precision vs. Accuracy in Star Catalogs." Symposium - International Astronomical Union 166 (1995): 372. http://dx.doi.org/10.1017/s0074180900228556.

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As better precision is achieved and more sophisticated reduction methods are created previously invisible biases surface. This has been especially true in astrometric Schmidt plate work. The problem of their amelioration is not fully solved and precision per se is meaningless in the presence of poor accuracy of comparable amplitude. Continuing to benignly neglect this issue puts us in the position of standing on only one statistical leg. New techniques have been designed to further minimize systematic errors. Of especial interest to star catalog analysis is the method of infinitely overlapping

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40

Le, Huiling. "Random spherical triangles II: Shape densities." Advances in Applied Probability 21, no. 3 (1989): 581–94. http://dx.doi.org/10.2307/1427637.

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This paper gives the exact evaluation of the shape density on the shape space Σ(S2, 3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a ‘cap' of S2 bounded by a ‘small' circle of angular radius ρ0.

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41

Kulkarni, Sanjay B., та Sandeep Kulkarni. "Study of the Value of π Probability Sampling by Testing Hypothesis and Experimentally". Journal of Computers, Mechanical and Management 3, № 1 (2024): 22–29. http://dx.doi.org/10.57159/gadl.jcmm.3.1.240101.

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This study evaluated the value of π using the Monte Carlo Simulation Method and compared the results with experimental values. The experimental value of π was determined by considering a unit circle |z| = 1 centered at the origin, inscribed within a square with vertices (0, 0), (1, 0), (1, 1), and (0, 1). Points were randomly generated within the square, where points satisfying |z| ≤ 1 lay within the circle, and those with |z| ≥ 1 lay outside the circle but within the square. By selecting large numbers of random pairs and determining their positions relative to the circle, the ratio π = 4n/N w

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42

Le, Huiling. "Random spherical triangles II: Shape densities." Advances in Applied Probability 21, no. 03 (1989): 581–94. http://dx.doi.org/10.1017/s0001867800018826.

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This paper gives the exact evaluation of the shape density on the shape space Σ(S 2, 3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a ‘cap' of S2 bounded by a ‘small' circle of angular radius ρ 0 .

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43

NAKANO, Yushi. "Historic Behaviour for Random Expanding Maps on the Circle." Tokyo Journal of Mathematics 40, no. 1 (2017): 165–84. http://dx.doi.org/10.3836/tjm/1502179221.

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44

Michelen, Marcus. "Real roots near the unit circle of random polynomials." Transactions of the American Mathematical Society 374, no. 6 (2021): 4359–74. http://dx.doi.org/10.1090/tran/8379.

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45

Bazarova, Alina, István Berkes, and Marko Raseta. "On the Discrepancy of Random Walks on the Circle." Uniform distribution theory 14, no. 2 (2019): 73–86. http://dx.doi.org/10.2478/udt-2019-0015.

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AbstractLet X1,X2,... be i.i.d. absolutely continuous random variables, let {S_k} = \sum\nolimits_{j = 1}^k {{X_j}} (mod 1) and let D*N denote the star discrepancy of the sequence (Sk)1≤k≤N. We determine the limit distribution of \sqrt N D_N^* and the weak limit of the sequence \sqrt N \left( {{F_N}(t) - t} \right) in the Skorohod space D[0, 1], where FN (t) denotes the empirical distribution function of the sequence (Sk)1≤k≤N.

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46

Blank, Michael. "Ergodicity of a collective random walk on a circle." Nonlinearity 27, no. 5 (2014): 953–71. http://dx.doi.org/10.1088/0951-7715/27/5/953.

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47

Fjeldso, N., J. Midtdal, and F. Ravndal. "Random walks of a quantum particle on a circle." Journal of Physics A: Mathematical and General 21, no. 7 (1988): 1633–47. http://dx.doi.org/10.1088/0305-4470/21/7/027.

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48

Li, Weigu, and Kening Lu. "Rotation numbers for random dynamical systems on the circle." Transactions of the American Mathematical Society 360, no. 10 (2008): 5509–28. http://dx.doi.org/10.1090/s0002-9947-08-04619-9.

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49

Huang, Chunfeng, Haimeng Zhang, and Scott M. Robeson. "Intrinsic random functions and universal kriging on the circle." Statistics & Probability Letters 108 (January 2016): 33–39. http://dx.doi.org/10.1016/j.spl.2015.09.023.

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50

Auer, Peter. "The circle homogeneously covered by random walk on 2." Statistics & Probability Letters 9, no. 5 (1990): 403–7. http://dx.doi.org/10.1016/0167-7152(90)90032-3.

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