<< /Length 11 0 R /Filter /FlateDecode >> 4, 2013, pp. 16, no.3, 1988, pp.1229-1241. The material covered here is considered in much greater depth in the follow-ing excellent texts. K. Marton, Bounding d-distance by information divergence, The Annals of Probability, vol.24, 1996, pp. stream Course description: This is a graduate-level introduction to probabilistic reasoning for discrete systems. x���J�0��}��LAcs��f�8Aq4�B\�c�j�e�"�3��f��È0d�¹�=g�%6��т`,��xB�+a8 %��QS��&�%'i�ָp[��7w��ۓ$ϥ��4�0�+[@J�y�L �����,���c]6��R����zn��9�&]p� �Vq�� Namely, to the probability of the corresponding outcome. Most topics of the course are covered in the book by Pierre Brémaud referenced as [B17] below. No attempt is made at covering these areas in depth. If a random variable can take only finite set of values (Discrete Random Variable), then its probability distribution is called as Probability Mass Function or PMF. on Foundations of Computer Science, 1996, pp. 12 0 obj Looking at this table we can see that the greatest probability is \(P\begin{pmatrix}X = 6 \end{pmatrix} = \frac{36}{90}\). The concentration of the chromatic number of random graphs Combinatorica, vol. MAT 589 Topics in Probability, Statistics and Dynamics: Modern discrete probability theory (Spring 2017) Instructor Allan Sly (asly@princeton) Class time 9:30-11:00 on Tuesdays and Thursdays at 401 Fine Hall. 5. 1, 1990, pp.115-130. endobj 5 0 obj 20. /Rotate 0 >> E-mails: abarg at umd dot edu and elishco at gmail dot com Class times: Lectures: Monday, Wednesday 12:30 - 1:45pm, AJC2121 Instructor availability outside class hours: Please … These lecture notes form the basis for a one-semester introduction to modern dis-crete probability with an emphasis on essential techniques used throughout the field. Random walks and Markov chains. 21. Throughout the paper we … 5130-5140). �v ���}�-�s�ehn�6B��}�tKnd�G�]��*���m�L}>t��Ӂ� A�P�B���� ��R�5]~]�>V'�Y��Qv`- �P}� The class will focus on specific systems, and one of the central topics will be threshold behavior. Generating random spanning trees more quickly than the cover time, Proc. Sebastien Roch, UW–Madison´ Modern Discrete Probability – Models and Questions. 293-307. 11. 5, pp. As far as the discrete methodologies in Statistics are concerned, our interest is focused on the foundations and applications of the Experimental Design Theory. The list of papers is given below. IEEE Trans. P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithm, Journal of Computer and System Sciences, Volume 57, Issue 1, August 1998, Pages 20-36. Theory of Computing (STOC), pages 296â303. 12. The above model can be found e.g. N. Madras and D. Randall, Factoring graphs to bound mixing rates, Prov. 209, no. Rigorous location of phase transitions in hard optimization problems, Nature, vol.435, 2005, pp.759â764. … Chen and L. Saloff-Coste, Comparison of cutoffs between lazy walks and Markovian semigroups, Journal of Applied Probability, vol. 3. 25, no.1-2, 2005, pp. The concepts will be recalled as needed in class.). 7. 4 0 obj stream 93, no. D. B. Wilson. 9 0 obj 9. 14 0 obj Presentation topics and materials will be distributed halfway into the course. It is expected that only one student from each group will give the presentation; however, it is imperative that the entire group takes active role in preparing it. endobj '�e`�o��8�¿��ܪF
�[k��Хn�S�2�9Փ�VU��2��t u List of papers G.-Y. stream Lectures: Monday, Wednesday 12:30 - 1:45pm, AJC2121 Class times: Foundations Comp. 17. 10 0 obj 3, 1972, pp.328-345. E-mails: abarg at umd dot edu and elishco at gmail dot com 8. Student presentations1. R. Pemantle, Phase Transition in Reinforced Random Walk and RWRE on Trees, The Annals of Probability, vol. 13. D. Achlioptas, A. Naor, and Y. Peres. Prerequisites Good knowledge of undergraduate probability theory on the level of STAT410 or ENEE620 (Chapters 1 and 2 in [B17] should suffice as an introduction. Directed graphs. Probability Distribution of discrete random variable is the list of values of different outcomes and their respective probabilities. 153, no. Course contents: A subset of the following topics will be covered: Home assignments: | Problem set 1 (by 10/2) | Problem set 2 (by 11/4) | Problem set 3 (by 12/4) | Final (by 12/16) | Room 405 Fine Hall. �XT,��RC�N@�'!~�iBBE�؞;s��l0�ԝ�q$�Ux@�s��dqm��+�8IB�F$9� Textbook: The lectures draw on multiple sources. Otherwise, please send one of us an email. 2, 1988, pp. Course Homepage: http://www.ece.umd.edu/~abarg/MDP. Discrete Probability Distributions, Essentials of Modern Business Statistics - David R. Anderson, Dennis J. Sweeney,Thomas A. Williams | All the textbook answe… 4. We will cover the classic results and arguments of Percolation. Modern Discrete Probability VI - Spectral Techniques Background Sebastien Roch´ UW–Madison Mathematics December 1, 2014 Sebastien Roch, UW–Madison´ Modern Discrete Probability – Spectral Techniques. L. Shepp, Covering the circle with random arcs, Israel Journal of Mathematics, vol.11, no. 1. So the mode is \(6\). 2. A method of calculating exact ruin probabilities in discrete time models 309 S(0) = u and S(n)= u+γn− X i i=1 n ∑, n∈N. x�Zْ�F}�Wt��wԋ�. N. Alon and M. Krivelevich. 489â509. 22. 8, no. We will have two dates for presentation: Friday Dec. 6 and Tuesday Dec. 10 (time and place are given in the shared Excel sheet). Fall 2019. D. Aldous and B. Flannery, Two applications of urn processes, Probability in the Engineering and Informational Sciences, vol. 3, pp.696-750. << /ProcSet [ /PDF /Text ] /Font << /Ty2 8 0 R /Ty1 7 0 R >> >> << /Type /Page /Parent 3 0 R /Resources 12 0 R /Contents 10 0 R /MediaBox D. Aldous and P. Diaconis, Shuffling cards and stopping times, The American Mathematical Monthly, vol. The basic idea is that in discrete probability models we can compute the probability of events by adding all the corresponding outcomes, while in continuous probability models we need to use integration instead of summation. 82, 1989, pp. Your presentation should be 17min long (this may change later depending on the number of groups) and prepared on slides. x���N�0E����L$0����G7H Your task is to present a problem and explain a solution, summarizing the main steps of the proof. in the papers by Rolski et al.,5 Klugman et al.,6 Gajek7 or Gajek and Rudź8 among many others. This will be our main textbook. Instructors : Alexander Barg, Ohad Elishco Department of Electrical and Computer Engineering/Institute for Systems Research Office: 2361 A.V.Williams Building. 1, 1981, pp.1-12. 10. We will cover several foundational models tools used in the analysis. 194-203. M. Ajtai, J. Komlos, and E. Szemeredi, The longest path in a random graph, Combinatorica, vol. endobj This function maps every element of a random variable’s sample space to a real number in the interval [0, 1]. %PDF-1.3 1997 ACM Sympos. 333â348. Authors (view affiliations) Pierre Brémaud; Textbook. 16. endobj The goal of these notes is to give an introduction to fundamental models and techniques in graduate-level modern discrete probability. Description. 3, 2010, pp. Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. 18. The discrete random variable's mode is the value that \(X\) is most likely to take-on. The aim of this course is to survey some of the fundamentals of modern discrete probability, particularly random processes on networks and discrete structures. Buy eBook. Modern Discrete Probability I - Introduction Stochastic processes on graphs: models and questions Sebastien Roch´ UW–Madison Mathematics August 31, 2020 Sebastien Roch, UW–Madison´ Modern Discrete Probability – Models and Questions.
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