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1

Martino, Luca, David Luengo, and Joaquín Míguez. Independent Random Sampling Methods. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72634-2.

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2

Skorohod, A. V. Random Processes with Independent Increments. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3710-2.

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3

Skorokhod, A. V. Random processes with independent increments. Kluwer Academic Publishers, 1991.

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4

Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. Cambridge University Press, 1994.

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5

M, Lee Lawrence, Nicol David, and United States. National Aeronautics and Space Administration., eds. On the minimum of independent geometrically distributed random variables. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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6

Arak, T. V. Uniform limit theorems for sums of independent random variables. American Mathematical Society, 1988.

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7

Petrov, V. V. Limit theorems of probability theory: Sequences of independent random variables. Clarendon Press, 1995.

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8

Zaihraiev, Oleksandr. Large-deviation theorems for sums of independent and identically distributed random vectors. Wydawn. Uniwersytetu Mikolaja Kopernika, 2005.

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9

Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. John Wiley & Sons, 2001.

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10

Ni, Jian. Connectivity, dynamic performance of random radio networks and state independent uniquely decodable codes: Codeword synchronisation of collaborative coding multiple access communications. typescript, 1994.

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11

Sigal, Anatoliy. Probability theory with elements of mathematical statistics, theory of random processes and econometrics. INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/1842523.

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The textbook outlines the main sections of probability theory, mathematical statistics, theory of random processes and econometrics. The presentation of theoretical information is illustrated by numerous numerical examples. It contains questions and tasks for students to self-check the degree of assimilation of the material presented, as well as tasks for independent solution.
 Meets the requirements of the federal state educational standards of higher education of the latest generation.
 For students of higher educational institutions studying in the field of training "Business Info
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12

Luby, Michael George. Pairwise independence and derandomization. Now, 2007.

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13

Lemeshko, Boris, and Irina Veretel'nikova. Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1587437.

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The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the applic
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14

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. American Mathematical Society, 2016.

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15

Martino, Luca, David Luengo, and Joaquín Míguez. Independent Random Sampling Methods. Springer, 2019.

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16

Martino, Luca, David Luengo, and Joaquín Míguez. Independent Random Sampling Methods. Springer, 2018.

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17

Sums of Independent Random Variables. Springer, 2011.

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18

Skorohod, A. V. Random Processes with Independent Increments. Springer, 2012.

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19

Skorohod, A. V. Random Processes with Independent Increments. Springer, 1991.

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20

Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. de Gruyter GmbH, Walter, 2022.

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21

Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. Springer, 2011.

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22

Braverman, Michael Sh. Independent Random Variables and Rearrangement Invariant Spaces. Cambridge University Press, 2010.

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23

Braverman, Michael Sh. Independent Random Variables and Rearrangement Invariant Spaces. Cambridge University Press, 2011.

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24

Hans, James. True Random Numbers Under 100: Independent Simulations. Independently Published, 2021.

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25

Independent random variables in rearrangement invariant spaces: Report. Far-Easte[r]n Branch of the Academy of Sciences of the USSR, 1990.

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26

Gnedenko, B. V. Limit distributions for sums of independent random variables. 2nd ed. Wiley, 1994.

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27

Gnedenko, B. V., K. L. Chung, and A. N. Kolmogorov. Limit Distributions for Sums of Independent Random Variables. Martino Fine Books, 2021.

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28

Korolev, V. Y., and V. M. Zolotarev. Limit Distributions for Sums of Independent Random Variables. Brill Academic Pub, 2007.

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29

A. N. (Andreĭ Nikolaevich) Kolmogorov and B. V. (Boris Vladimirovich) Gnedenko. Limit Distributions for Sums of Independent Random Variables. Creative Media Partners, LLC, 2021.

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30

A. N. (Andreĭ Nikolaevich) Kolmogorov and B. V. (Boris Vladimirovich) Gnedenko. Limit Distributions for Sums of Independent Random Variables. Creative Media Partners, LLC, 2021.

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31

Independent Component Analysis: Algorithms, Applications and Ambiguities. Nova Science Pub Inc., 2018.

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32

Zinn-Justin, Jean. From Random Walks to Random Matrices. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.001.0001.

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Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models and, in consequence, develops our understanding of the fundamental nature of the universe. This book offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic, and develops the discussion in a self-contained manner. At the same time, the selected topics have common themes running throughout the book, which connect the i
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33

Gardner, William A. The Random Processes Tutor: A Comprehensive Solutions Manual for Independent Study. Mcgraw-Hill College, 1990.

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34

Comtet1, Alain, and Yves Tourigny2. Impurity models and products of random matrices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0011.

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This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2×2 case. The notion of impurity model—that is, a system in which the interactions are highly localized—links the two themes and enables their study by elementary mathematical tools. After discussing the spectral theory of some impurity models, Furstenberg’s theorem is stated and illustrated, which gives sufficient conditions for the exponential growth of a product of independent, identically distributed matrices.
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35

Butyrskiy, Evgeniy. Methods for modeling and estimating random variables and processes. Strategy of the Future, 2020. http://dx.doi.org/10.37468/mon_1850.

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The monograph introduces the basics of theory and practice of mathematical research methods of stochastic systems and processes. It examines the models, methods of describing and forming random events, values and processes, as well as methods of their optimal and suboptimal assessment. The monograph can be useful for a wide range of specialists in various fields of expertise in mathematical and statistical modeling in their research, and can also be used in the learning process to conduct both classroom, and independent theoretical and practical classes with students and masters of St. Petersb
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36

Meerschaert, Mark M., and Hans-Peter Scheffler. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice (Wiley Series in Probability and Statistics). Wiley-Interscience, 2001.

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37

Sub-Independence: A Useful Concept. Nova Science Publishers Inc., 2015.

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38

Hamedani, G. G., and Mehdi Maadooliat. Sub-Independence: A Useful Concept. Nova Science Publishers, Incorporated, 2015.

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39

Bellhouse, David. Probability and Its Application in Britain during the 17th and 18th Centuries. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.5.

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In the 18th and 19th centuries, probability was a part of moral and natural sciences, rather than of mathematics. Still, since Laplace’s 1812 Théorie analytique des probabilités, specific analytic methods of probability aroused the interest of mathematicians, and probability began to develop a purely mathematical quality. In the 20th century the mathematical essence reached full autonomy and constituted “modern” probability. Significant in this development was the gradual introduction of a measure theoretic framework. In this way, the main subfields of modern probability, as axiomatics, weak a
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40

Male, Camille. Traffic Distributions and Independence: Permutation Invariant Random Matrices and the Three Notions of Independence. American Mathematical Society, 2021.

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41

Luby, Michael, and Avi Wigderson. Pairwise Independence and Derandomization (Foundations and Trends(R) in Theoretical Computer Science). Now Publishers Inc, 2006.

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42

Geometry of Conditional Independence. University of California, Berkeley, 2007.

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43

Gladstein, Mimi R. The New Ayn Rand Companion. 2nd ed. Greenwood, 1999. http://dx.doi.org/10.5040/9798400690730.

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An essential guide to the life and works of Ayn Rand, the book chronicles and summarizes her writings, presents information about her national and global impact—and the response to it—and provides the most comprehensive bibliography published to date. Written by an independent scholar who is not part of either the Ayn Rand establishment or the Ayn Rand detractor camp,The New Ayn Rand Companionbuilds on the foundation of the original. New materials about Rand's posthumous publications, the latest biographical information, and summaries of books and articles about Rand, published since her death
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44

Zirnbauer, Martin R. Symmetry classes. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.3.

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This article examines the notion of ‘symmetry class’, which expresses the relevance of symmetries as an organizational principle. In his 1962 paper The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics, Dyson introduced the prime classification of random matrix ensembles based on a quantum mechanical setting with symmetries. He described three types of independent irreducible ensembles: complex Hermitian, real symmetric, and quaternion self-dual. This article first reviews Dyson’s threefold way from a modern perspective before considering a minimal extens
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45

Guionnet, Alice. Free probability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0003.

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Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion, stochastic differential calculus, entropy, etc. It also appears as the natural setup for studying large random matrices as their size goes to infinity and hence is central in the study of random matrices as their size go to infinity. In this chapter the
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46

Cicerone, Carol M., and Donald D. Hoffman. Illusory Color Spread from Apparent Motion. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0042.

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Color from motion describes the perception of subjective color that spreads over physically achromatic regions that are seen in apparent motion. Multiple frames are shown in quick succession, each frame composed of a random placement of differently colored dots on an achromatic background. From frame to frame, the locations of all dots are fixed, whereas the color assignments of dots in the test region change. Subjective color can be measured by color matches to and cancellation by real lights, can be seen with chromaticity differences alone in test and surround dots, and is independent of con
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47

Scarani, Valerio. Bell Nonlocality. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198788416.001.0001.

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Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted
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48

Butyrskiy, Evgeniy, and Alexandr Matveev. Mathematical modeling of systems and processes. Strategy of the Future, 2022. http://dx.doi.org/10.37468/book_011222.

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The monograph considers the fundamentals of systems theory and mathematical modeling using the principles of the systems approach. In the monograph, much attention is paid to set-theoretic, dynamic, as well as aggregative and combined models. Based on the group-theoretical approach, a generalization of the theory of signals, their characteristics are considered, their classification and some theorems are carried out. A separate chapter is devoted to mathematical models of signal interaction with the propagation medium. The monograph also considers mathematical models of stochastic signal proce
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49

Adams, Karen Ruth. The Causes of War. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190846626.013.323.

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The scientific study of war is a pressing concern for international politics. Given the destructive nature of war, ordinary citizens and policy makers alike are eager to anticipate if not outright avoid outbreaks of violence. Understanding the causes of war can be a complex process. Scholars of international relations must first define war, and then establish a universe of actors or conflicts in which both war and peace are possible. Next, they must collect data on the incidence of war in the entire universe of cases over a particular period of time, a random sample of relevant cases, a number
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50

Jet, Mark. Random Coloring Book: Black and White Line Drawings Explore Concepts Like Bravery, Beauty, Strength, Creativity, Independence and More. Independently Published, 2020.

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