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1

Kubilius, Jonas. Analiziniai ir tikimybiniai metodai skaičių teorijoje: Trečiosios tarptautines konferencijos J. Kubiliaus garbei darbų rinkinys / redaktoriai, A. Dubickas, A. Laurinčikas, E. Manstavičius = Analytic and probabilistic methods in number theory : proceedings of the third international conference in honour of J. Kubilius, Palanga, Lithuania, 24-28 September 2001. Vilnius: TEV, 2002.

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2

Jonas, Kubilius, Laurinčikas Antanas, Manstavičius E, and Stakėnas V, eds. Analytic and probabilistic methods in number theory: Proceedings of the second international conference in honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996. Vilnius, Lithuania: TEV, 1997.

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3

Tenenbaum, Gerald. Introduction à la théorie analytique et probabiliste des nombres. 2nd ed. Paris: Société Mathématique de France, 1995.

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4

Laurincikas, E., E. Manstavicius, and V. Stakenas, eds. Analytic and Probabilistic Methods in Number Theory. Berlin, Boston: DE GRUYTER, 1997. http://dx.doi.org/10.1515/9783110944648.

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5

1940-, Zhang Wen-Bin, ed. Number theory arising from finite fields: Analytic and probabilistic theory. New York: Marcel Dekker, 2001.

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6

Boultbee, R. Rounded numbers. [Toronto, Ont.?: s.n.], 1990.

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7

Japan) International Conference "Functions in Number Theory and Their Probabilistic Aspects" (2010 Kyoto. Functions in Number Theory and Their Probabilistic Aspects, December 13-17, 2010. Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University, 2012.

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8

Florian, Luca, ed. Analytic number theory: Exploring the anatomy of integers. Providence, R.I: American Mathematical Society, 2012.

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9

1956-, Applebaum David, Schürmann Michael 1955-, and Franz Uwe, eds. Quantum independent increment processes. Berlin: Springer, 2005.

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10

E, Barndorff-Nielsen O., Schürmann Michael, and Franz Uwe, eds. Quantum independent increment processes. Berlin: Springer, 2006.

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11

Random Matrices AMS Short Course. Modern aspects of random matrix theory: AMS Short Course, Random Matrices, January 6-7, 2013, San Diego, California. Edited by Vu, Van, 1970- editor of compilation. Providence, Rhode Island: American Mathematical Society, 2014.

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12

Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. Providence, Rhode Island: American Mathematical Society, 2016.

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13

Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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14

Kowalski, Emmanuel. Introduction to Probabilistic Number Theory. Cambridge University Press, 2021.

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15

Kowalski, Emmanuel. Introduction to Probabilistic Number Theory. University of Cambridge ESOL Examinations, 2021.

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16

Kowalski, Emmanuel. Introduction to Probabilistic Number Theory. Cambridge University Press, 2021.

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17

Re, Christopher, Dan Suciu, Dan Olteanu, and Christoph Koch. Probabilistic Databases. Springer International Publishing AG, 2011.

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18

Tenenbaum, G. Introduction to Analytic and Probabilistic Number Theory. University of Cambridge ESOL Examinations, 2000.

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19

P.D.T.A. Elliott. Probabilistic Number Theory II: Central Limit Theorems. Springer London, Limited, 2012.

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20

Schweiger, F., and E. Manstavičius, eds. Analytic and Probabilistic Methods in Number Theory. De Gruyter, 1992. http://dx.doi.org/10.1515/9783112314234.

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21

P. D. T. A. Elliott. Probabilistic Number Theory I: Mean-Value Theorems. Springer New York, 2011.

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22

P.D.T.A. Elliott. Probabilistic Number Theory II: Central Limit Theorems. Springer, 2011.

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23

P.D.T.A. Elliott. Probabilistic Number Theory I: Mean-Value Theorems. Springer London, Limited, 2012.

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24

Probabilistic Number Theory I: Mean-Value Theorems. Springer, 2011.

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25

Introduction to analytic and probabilistic number theory. Cambridge: Cambridge University Press, 1995.

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26

Introduction to analytic and probabilistic number theory. Springer, 2015.

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27

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. Taylor & Francis Group, 2001.

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28

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. Taylor & Francis Group, 2001.

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29

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. Taylor & Francis Group, 2001.

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30

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. Taylor & Francis Group, 2001.

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31

Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. CRC Press LLC, 2001.

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32

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory. Taylor & Francis Group, 2001.

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33

Gut, Allan. Probability: A Graduate Course (Springer Texts in Statistics). Springer, 2007.

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34

Zhang, Wen-Bin, and John Knopfmacher. Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory (Lecture Notes in Pure and Applied Mathematics). CRC, 2001.

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35

Manstavicius, E., and F. Schweiger. Analytic and Probabilistic Methods in Number Theory: Proceedings of the International Conference in Honour of J. Kubilius, Palanga, Lithuania, 24-28 September 1991. de Gruyter GmbH, Walter, 1992.

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36

Manstavicius, E. Analytic And Probabilistic Methods in Number Theory: Proceedings of the International Conference in Honour of J. Kubilius (New Trends in Probability and Statistics). Brill Academic Publishers, 1992.

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37

Manstavicius, E., E. Laurincikas, and V. Stakenas. Analytic and Probabilistic Methods in Number Theory: Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996. de Gruyter GmbH, Walter, 2012.

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38

Beck, József. Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting. Springer, 2016.

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39

Beck, József. Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting. Springer, 2014.

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40

Barndorff-Nielsen, O. E. Quantum Independent Increment Processes II: Structure of Quantum Lévy Processes, Classical Probability, and Physics (Lecture Notes in Mathematics). Springer, 2006.

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41

Schweiger, F., and E. Manstavičius. Analytic and Probabilistic Methods in Number Theory: Proceedings of the International Conference in Honour of J. Kubilius, Palanga, Lithuania, 24-28 September 1991. de Gruyter GmbH, Walter, 2020.

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42

Analytic and Probabilistic Methods in Number Theory: Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996. De Gruyter, Inc., 1997.

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43

(Editor), Jonas Kubilius, Antanas Laurincikas (Editor), E. Manstavicius (Editor), and V. Stakenas (Editor), eds. Analytic & Probabilistic Methods in Number Theory: Proceedings of the 2nd International Conference in Honour of J. Kubilius, Lithuania, 23-27 September ... Trends in Probability & Statistics , Vol 4). Brill Academic Publishers, 1997.

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44

Analytic and probabilistic methods in number theory: Proceedings of the second international conference in honour of J. Kubilius, Palanga, Lithuania, 23-27 ... (New trends in probability and statistics). VSP, 1997.

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45

Sampling in Combinatorial and Geometric Set Systems. American Mathematical Society, 2022.

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46

Thurner, Stefan, Rudolf Hanel, and Peter Klimekl. Probability and Random Processes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821939.003.0002.

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Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.
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47

Harmonic Analysis. American Mathematical Society, 2018.

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48

Vanden-Eijnden, Eric, Weinan E, and Tiejun Li. Applied Stochastic Analysis. American Mathematical Society, 2019.

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49

Applied Stochastic Analysis. American Mathematical Society, 2019.

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50

Galavotti, Maria Carla. The Origins of Probabilistic Epistemology. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.8.

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The notion of probability received great attention from 20th-century mathematicians and philosophers alike. This chapter focusses on a number of thinkers who not only devoted great efforts to the notion of probability and its foundations, but also developed a thoroughly probabilistic epistemological perspective. Special attention will be paid to Hans Reichenbach, Harold Jeffreys, and Bruno de Finetti. Although these authors embraced diverging interpretations of probability, namely frequentism in the case of Reichenbach, logicism in the case of Jeffreys, and subjectivism in the case of de Finetti, they shared the conviction that probability is an essential ingredient not just of science, but of human knowledge at large, and laid the foundations of a probabilistic approach to epistemology that is today mainstream.
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