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1

Percus, O. E. Random number generators for ultracomputers. New York: Courant Institute of Mathematical Sciences, New York University, 1987.

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2

István, Deák. Random number generators and simulation. Budapest: Akadémiai Kiadó, 1990.

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3

Kollmitzer, Christian, Stefan Schauer, Stefan Rass, and Benjamin Rainer, eds. Quantum Random Number Generation. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-72596-3.

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4

Lewis, Peter A. W. Graphical analysis of some pseudo-random number generators. Monterey, Calif: Naval Postgraduate School, 1986.

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5

M, Kelsey John, and Information Technology Laboratory (National Institute of Standards and Technology). Computer Security Division, eds. Recommendation for random number generation using deterministic random bit generators (revised). Gaithersburg, MD]: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, Computer Security Division, Information Technology Laboratory, 2007.

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6

Peter, Hellekalek, and Larcher Gerhard, eds. Random and quasi-random point sets. New York: Springer, 1998.

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7

Random number generation and Monte Carlo methods. New York: Springer, 1998.

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8

Random number generation and Monte Carlo methods. 2nd ed. New York: Springer-Verlag, 2003.

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9

Karmakar, Debashis. Random number generators (RNG) and their testing for sequential programmes. Mumbai: Bhabha Atomic Research Centre, 2002.

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10

Nisan, Noam. Using hard problems to create pseudorandom generators. Cambridge, Mass: MIT Press, 1992.

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11

Alonso, Laurent. Random generation of trees: Random generators in computer science. Boston: Kluwer Academic, 1995.

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12

István, Deák. Véletlenszám-generátorok és alkalmazásuk. Budapest: Akadémiai Kiadó, 1986.

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13

L, Rukhin Andrew, and National Institute of Standards and Technology (U.S.), eds. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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14

Rukhin, Andrew L. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, MD: U.S. Dept. of Commerce, National Institute of Standards and Technology, 2008.

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15

L, Rukhin Andrew, and National Institute of Standards and Technology (U.S.), eds. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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16

L, Rukhin Andrew, and National Institute of Standards and Technology (U.S.), eds. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, Md: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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17

L, Rukhin Andrew, and National Institute of Standards and Technology (U.S.), eds. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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18

Uniform random numbers: Theory and practice. Boston, Mass: Kluwer Academic Publishers, 1995.

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19

Random number generation and quasi-Monte Carlo methods. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

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20

Pseudorandomness and cryptographic applications. Princeton, NJ: Princeton University Press, 1996.

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21

Niederreiter, Harald. Random numbergeneration and quasi-Monte Carlo methods. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

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22

Analytic methods in the analysis and design of number-theoretic algorithms. Cambridge, Mass: MIT Press, 1985.

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23

Ciric, Aleksandar. A Guide to Monte Carlo and Quantum Monte Carlo methods : Quantum Monte Carlo: Variational and Diffusion; MC in general; Markov Chain; Statistics; Random number generators; Hidden Monte Carlo. Createspace Independent Publishing Platform, 2016.

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24

Hellekalek, P., P. Hickernell, Gerhard Larcher, J. Beck, and Peter Hellekalek. Random and Quasi-Random Point Sets. Springer London, Limited, 2012.

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25

Nisan, Noam. Using Hard Problems to Create Pseudorandom Generators. MIT Press, 2003.

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26

Kollmitzer, Christian, Stefan Schauer, Stefan Rass, and Benjamin Rainer. Quantum Random Number Generation: Theory and Practice. Springer, 2020.

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27

A Primer On Pseudorandom Generators. American Mathematical Society(RI), 2010.

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28

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 by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.
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29

Gentle, James E. Random Number Generation and Monte Carlo Methods (Statistics and Computing). Springer, 2004.

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30

Schott, René, and Laurent Alonso. Random Generation of Trees: Random Generators in Computer Science. Springer, 1994.

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31

Moeschlin, Otto, and Eugen Grycko. Experimental Stochastics in Physics. Springer, 2006.

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32

National Aeronautics and Space Administration (NASA) Staff. Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications. Independently Published, 2019.

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33

Uniform Random Numbers. Springer My Copy UK, 1995.

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34

Tezuka, Shu. Uniform Random Numbers. Springer, 2012.

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35

Johnston, David. Random Number Generators--Principles and Practices: A Guide for Engineers and Programmers. De Gruyter, Inc., 2018.

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36

Johnston, David. Random Number Generators-Principles and Practices: A Guide for Engineers and Programmers. De|G Press, 2018.

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37

Johnston, David. Random Number Generators-Principles and Practice: A Guide for Engineers and Programmers. De Gruyter, Inc., 2018.

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38

Moeschlin, Otto, Claudia Pohl, Frank Steinert, and Eugen Grycko. Experimental Stochastics. 2nd ed. Springer, 2003.

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39

Experimental Stochastics. Springer-Verlag Telos, 1997.

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40

Tezuka, Shu. Uniform Random Numbers: Theory and Practice. Springer London, Limited, 2012.

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41

Niederreiter, Harald. Random Number Generation and Quasi-Monte Carlo Methods (CBMS-NSF Regional Conference Series in Applied Mathematics). Society for Industrial Mathematics, 1987.

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42

Bilan, Stepan. Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators: Emerging Research and Opportunities. IGI Global, 2017.

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43

Tlelo-Cuautle, Esteban, José de Jesús Rangel-Magdaleno, and Luis Gerardo de la Fraga. Engineering Applications of FPGAs: Chaotic Systems, Artificial Neural Networks, Random Number Generators, and Secure Communication Systems. Springer London, Limited, 2016.

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44

Tlelo-Cuautle, Esteban, José de Jesús Rangel-Magdaleno, and Luis Gerardo de la Fraga. Engineering Applications of FPGAs: Chaotic Systems, Artificial Neural Networks, Random Number Generators, and Secure Communication Systems. Springer, 2018.

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45

Tlelo-Cuautle, Esteban, José de Jesús Rangel-Magdaleno, and Luis Gerardo de la Fraga. Engineering Applications of FPGAs: Chaotic Systems, Artificial Neural Networks, Random Number Generators, and Secure Communication Systems. Springer, 2016.

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46

Bohigas, Oriol, and Hans Weidenmuller. History – an overview. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.2.

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This article discusses the first four decades of the history of random matrix theory (RMT), that is, until about 1990. It first considers Niels Bohr's formulation of the concept of the compound nucleus, which is at the root of the use of random matrices in physics, before analysing the development of the theory of spectral fluctuations. In particular, it examines the Wishart ensemble; Dyson's classification leading to the three canonical ensembles — Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE), and Gaussian Symplectic Ensemble (GSE); and the breaking of a symmetry or an invariance. It also describes how random matrix models emerged from quantum physics, more specifically from a statistical approach to the strongly interacting many-body system of the atomic nucleus. The article concludes with an overview of data on nuclear resonances, many-body theory, chaos, number theory, scattering theory, replica trick and supersymmetry, disordered solids, and interacting fermions and field theory.
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47

Marks II, Robert J. Handbook of Fourier Analysis & Its Applications. Oxford University Press, 2009. http://dx.doi.org/10.1093/oso/9780195335927.001.0001.

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Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.
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