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1

Podczeck, Konrad, and Daniela Puzzello. "Independent random matching." Economic Theory 50, no. 1 (2010): 1–29. http://dx.doi.org/10.1007/s00199-010-0584-4.

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2

Suck, Reinhard. "Independent random utility representations." Mathematical Social Sciences 43, no. 3 (2002): 371–89. http://dx.doi.org/10.1016/s0165-4896(02)00020-3.

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3

Robert, Christian. "Independent Random Sampling Methods." CHANCE 32, no. 1 (2019): 62–63. http://dx.doi.org/10.1080/09332480.2019.1579592.

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4

Lutz, Jack H. "On independent random oracles." Theoretical Computer Science 92, no. 2 (1992): 301–7. http://dx.doi.org/10.1016/0304-3975(92)90317-9.

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5

Kruglov, V. M. "Weak Compactness of Random Sumsof Independent Random Variables." Theory of Probability & Its Applications 43, no. 2 (1999): 203–20. http://dx.doi.org/10.1137/s0040585x97976830.

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6

Hu, Tien-Chung. "On pairyise independent and independent exchangeable random variables." Stochastic Analysis and Applications 15, no. 1 (1997): 51–57. http://dx.doi.org/10.1080/07362999708809463.

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7

Suleymanov, Elchin. "Branching-independent random utility model." Journal of Economic Theory 220 (September 2024): 105880. http://dx.doi.org/10.1016/j.jet.2024.105880.

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8

Duffie, Darrell, and Yeneng Sun. "Existence of independent random matching." Annals of Applied Probability 17, no. 1 (2007): 386–419. http://dx.doi.org/10.1214/105051606000000673.

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9

Gallesco, Christophe. "Meeting time of independent random walks in random environment." ESAIM: Probability and Statistics 17 (2013): 257–92. http://dx.doi.org/10.1051/ps/2011159.

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10

Korolev, V. Yu. "Convergence of Random Sequences with Independent Random Indices II." Theory of Probability & Its Applications 40, no. 4 (1996): 770–72. http://dx.doi.org/10.1137/1140089.

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11

Korolev, V. Yu, and E. V. Kossova. "Convergence of multidimensional random sequences with independent random indices." Journal of Mathematical Sciences 76, no. 2 (1995): 2259–68. http://dx.doi.org/10.1007/bf02362696.

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12

Teerapabolarn, K. "Poisson approximation for random sums of independent binomial random variables." Applied Mathematical Sciences 8 (2014): 8643–46. http://dx.doi.org/10.12988/ams.2014.410813.

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13

Korolev, V. Yu. "Convergence of Moments of Random Sums of Independent Random Variables." Theory of Probability & Its Applications 30, no. 2 (1986): 386–90. http://dx.doi.org/10.1137/1130044.

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14

Korolev, V. Yu. "Convergence of Random Sequences with the Independent Random Indices I." Theory of Probability & Its Applications 39, no. 2 (1995): 282–97. http://dx.doi.org/10.1137/1139018.

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15

Wittmann, Rainer. "Superprophet inequalities for independent random variables." Journal of Applied Probability 33, no. 3 (1996): 904–8. http://dx.doi.org/10.2307/3215367.

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Streszczenie:
As well as having complete knowledge of the future, a superprophet can also alter the order of observation as it is presented to a player without foresight, whose strategy is known to the prophet. It is shown that a superprophet can only do twice as well as his counterpart, if the underlying random sequence is independent.
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16

Roehner, Bertrand, and Peter Winiwarter. "Aggregation of independent Paretian random variables." Advances in Applied Probability 17, no. 2 (1985): 465–69. http://dx.doi.org/10.2307/1427153.

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Empirical Paretian distributions play an important role in urban demography, size distributions of firms and income distributions; hence the addition of Paretian random variables is of interest. First, we give the asymptotic behavior (for large values of the variable) of the density function of a sum of n independently distributed Paretian variables. We then obtain the limiting distribution of an infinite sum of (i.i.d) Paretian variables and link our results with the theory of stable distributions.
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17

Braverman, Michael. "Independent Random Variables in Lorentz Spaces." Bulletin of the London Mathematical Society 28, no. 1 (1996): 79–87. http://dx.doi.org/10.1112/blms/28.1.79.

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18

Hombas, Vassilios C. "Combinations of Independent Normal Random Variables." Teaching Statistics 11, no. 3 (1989): 74–75. http://dx.doi.org/10.1111/j.1467-9639.1989.tb00065.x.

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19

Patterson, RichardF, and Ekrem Savaş. "Summability of Double Independent Random Variables." Journal of Inequalities and Applications 2008, no. 1 (2008): 948195. http://dx.doi.org/10.1155/2008/948195.

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20

Liu, Yang, Qi Zhao, Ming-Han Li, et al. "Device-independent quantum random-number generation." Nature 562, no. 7728 (2018): 548–51. http://dx.doi.org/10.1038/s41586-018-0559-3.

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21

Wittmann, Rainer. "Superprophet inequalities for independent random variables." Journal of Applied Probability 33, no. 03 (1996): 904–8. http://dx.doi.org/10.1017/s0021900200100294.

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As well as having complete knowledge of the future, a superprophet can also alter the order of observation as it is presented to a player without foresight, whose strategy is known to the prophet. It is shown that a superprophet can only do twice as well as his counterpart, if the underlying random sequence is independent.
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22

Roehner, Bertrand, and Peter Winiwarter. "Aggregation of independent Paretian random variables." Advances in Applied Probability 17, no. 02 (1985): 465–69. http://dx.doi.org/10.1017/s0001867800015093.

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Empirical Paretian distributions play an important role in urban demography, size distributions of firms and income distributions; hence the addition of Paretian random variables is of interest. First, we give the asymptotic behavior (for large values of the variable) of the density function of a sum of n independently distributed Paretian variables. We then obtain the limiting distribution of an infinite sum of (i.i.d) Paretian variables and link our results with the theory of stable distributions.
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23

Feng, Yuhu. "Sums of independent fuzzy random variables." Fuzzy Sets and Systems 123, no. 1 (2001): 11–18. http://dx.doi.org/10.1016/s0165-0114(00)00041-5.

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24

Dettmann, Carl P., and Orestis Georgiou. "Product of independent uniform random variables." Statistics & Probability Letters 79, no. 24 (2009): 2501–3. http://dx.doi.org/10.1016/j.spl.2009.09.004.

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25

O’Rourke, Sean, David Renfrew, Alexander Soshnikov, and Van Vu. "Products of Independent Elliptic Random Matrices." Journal of Statistical Physics 160, no. 1 (2015): 89–119. http://dx.doi.org/10.1007/s10955-015-1246-5.

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26

Maassen, Hans. "Addition of freely independent random variables." Journal of Functional Analysis 106, no. 2 (1992): 409–38. http://dx.doi.org/10.1016/0022-1236(92)90055-n.

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27

Letchikov, A. V. "Products of unimodular independent random matrices." Russian Mathematical Surveys 51, no. 1 (1996): 49–96. http://dx.doi.org/10.1070/rm1996v051n01abeh002735.

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28

Cox, J. Theodore, and Richard Durrett. "Large deviations for independent random walks." Probability Theory and Related Fields 84, no. 1 (1990): 67–82. http://dx.doi.org/10.1007/bf01288559.

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29

Coja-Oghlan, Amin, and Charilaos Efthymiou. "On independent sets in random graphs." Random Structures & Algorithms 47, no. 3 (2014): 436–86. http://dx.doi.org/10.1002/rsa.20550.

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30

Chang, Cheng-Shang, and Joy A. Thomas. "Huffman algebras for independent random variables." Discrete Event Dynamic Systems: Theory and Applications 4, no. 1 (1994): 23–40. http://dx.doi.org/10.1007/bf01516009.

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31

Kirkup, George A. "Random variables with completely independent subcollections." Journal of Algebra 309, no. 2 (2007): 427–54. http://dx.doi.org/10.1016/j.jalgebra.2006.06.023.

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32

Jiao, Yong, Fedor Sukochev, and Dmitriy Zanin. "Sums of independent and freely independent identically distributed random variables." Studia Mathematica 251, no. 3 (2020): 289–315. http://dx.doi.org/10.4064/sm180912-31-12.

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33

Jiao, Yong, Fedor Sukochev, Guangheng Xie та Dmitriy Zanin. "Φ-moment inequalities for independent and freely independent random variables". Journal of Functional Analysis 270, № 12 (2016): 4558–96. http://dx.doi.org/10.1016/j.jfa.2016.02.001.

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34

Alili, S. "Asymptotic behaviour for random walks in random environments." Journal of Applied Probability 36, no. 2 (1999): 334–49. http://dx.doi.org/10.1239/jap/1032374457.

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In this paper we consider limit theorems for a random walk in a random environment, (Xn). Known results (recurrence-transience criteria, law of large numbers) in the case of independent environments are naturally extended to the case where the environments are only supposed to be stationary and ergodic. Furthermore, if ‘the fluctuations of the random transition probabilities around are small’, we show that there exists an invariant probability measure for ‘the environments seen from the position of (Xn)’. In the case of uniquely ergodic (therefore non-independent) environments, this measure ex
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35

Alili, S. "Asymptotic behaviour for random walks in random environments." Journal of Applied Probability 36, no. 02 (1999): 334–49. http://dx.doi.org/10.1017/s0021900200017174.

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In this paper we consider limit theorems for a random walk in a random environment, (X n ). Known results (recurrence-transience criteria, law of large numbers) in the case of independent environments are naturally extended to the case where the environments are only supposed to be stationary and ergodic. Furthermore, if ‘the fluctuations of the random transition probabilities around are small’, we show that there exists an invariant probability measure for ‘the environments seen from the position of (X n )’. In the case of uniquely ergodic (therefore non-independent) environments, this measur
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36

Teerapabolarn, K. "A pointwise approximation for random sums of independent discrete random variables." Applied Mathematical Sciences 8 (2014): 8577–79. http://dx.doi.org/10.12988/ams.2014.410812.

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37

Hui, Stefen, and C. J. Park. "The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables." Communications in Statistics - Theory and Methods 43, no. 19 (2013): 4103–8. http://dx.doi.org/10.1080/03610926.2012.705941.

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38

Volodin, N. A. "Random summation of independent identically distributed random vectors with zero means." Journal of Soviet Mathematics 59, no. 4 (1992): 885–90. http://dx.doi.org/10.1007/bf01099114.

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39

Unnisa, Yaseen, Danh Tran, and Fu Chun Huang. "Statistical Independence and Independent Component Analysis." Applied Mechanics and Materials 553 (May 2014): 564–69. http://dx.doi.org/10.4028/www.scientific.net/amm.553.564.

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Independent Component Analysis (ICA) is a recent method of blind source separation, it has been employed in medical image processing and structural damge detection. It can extract source signals and the unmixing matrix of the system using mixture signals only. This novel method relies on the assumption that source signals are statistically independent. This paper looks at various measures of statistical independence (SI) employed in ICA, the measures proposed by Bakirov and his associates, and the effects of levels of SI of source signals on the output of ICA. Firstly, two statistical independ
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40

Feldman, G. M. "Independent Random Variables in Abelian Groups with Independent Sum and Difference." Theory of Probability & Its Applications 61, no. 2 (2017): 335–45. http://dx.doi.org/10.1137/s0040585x97t988198.

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41

Wang, Y. H. "Dependent Random Variables with Independent Subsets - II." Canadian Mathematical Bulletin 33, no. 1 (1990): 24–28. http://dx.doi.org/10.4153/cmb-1990-004-6.

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AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal dis
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42

Foran, James, and Lee Hart. "Independent Random Variables on the Unit Interval." Missouri Journal of Mathematical Sciences 6, no. 3 (1994): 144–46. http://dx.doi.org/10.35834/1994/0603144.

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43

Gordienko, Evgueni, and Juan Ruiz de Chávez. "Sums of Independent Random Vectors: Proximity Estimating." Stochastic Models 22, no. 4 (2006): 607–16. http://dx.doi.org/10.1080/15326340600878081.

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44

Carothers, N. L., and S. J. Dilworth. "Inequalities for sums of independent random variables." Proceedings of the American Mathematical Society 104, no. 1 (1988): 221. http://dx.doi.org/10.1090/s0002-9939-1988-0958071-4.

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45

Mongia, Vardaan, Abhishek Kumar, Shashi Prabhakar, Anindya Banerji, and R. P. Singh. "Investigating device-independent quantum random number generation." Physics Letters A 526 (November 2024): 129954. http://dx.doi.org/10.1016/j.physleta.2024.129954.

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46

Hou, Wanting, and Wenming Hong. "Minima of independent time-inhomogeneous random walks." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 03 (2020): 2050021. http://dx.doi.org/10.1142/s0219025720500216.

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In this paper, we will consider the minima of an exponentially growing number of independent time-inhomogeneous random walks, where the first- and second-order limit behaviors for the minima have been obtained.
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47

Gaposhkin, V. F. "Summability of Sequences of Independent Random Variables." Theory of Probability & Its Applications 33, no. 1 (1989): 62–74. http://dx.doi.org/10.1137/1133006.

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48

De Schuymer, B., H. De Meyer, and B. De Baets. "Cycle-transitive comparison of independent random variables." Journal of Multivariate Analysis 96, no. 2 (2005): 352–73. http://dx.doi.org/10.1016/j.jmva.2004.10.011.

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49

Grill, Karl. "Strassen-type laws for independent random walks." Stochastic Processes and their Applications 71, no. 1 (1997): 1–10. http://dx.doi.org/10.1016/s0304-4149(97)00043-4.

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50

Hollas, Boris. "Asymptotically independent topological indices on random trees." Journal of Mathematical Chemistry 38, no. 3 (2005): 379–87. http://dx.doi.org/10.1007/s10910-005-6474-5.

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