modern discrete probability
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D. Aldous and B. Flannery, Two applications of urn processes, Probability in the Engineering and Informational Sciences, vol. 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) | B. Recht, A simpler approach to matrix completion, arXiv:0910.0651 (Jounral of Machine Learning Research, vol.12, pp.3413-3430, 2011). 14. 5, pp. Looking at this table we can see that the greatest probability is \(P\begin{pmatrix}X = 6 \end{pmatrix} = \frac{36}{90}\). As you already know, a discrete probability distribution is specified by a probability mass function. Please team up into groups of two (a small number of groups of one is also permissible). Random graphs and networks. [0 0 612 792] /Rotate 0 >> If the problem is motivated by interesting applications, please do mention them, too. Instructors : Alexander Barg, Ohad Elishco The concentration of the chromatic number of random graphs Combinatorica, vol. '�e`�o��8�¿��ܪF �[k��Хn�S�2�9Փ�VU��2��t u Directed graphs. S. Blackburn and S. Gerke, Connectivity of the uniform random intersection graphs, arXiv:0805.2814 (Discrete Mathematics, vol. (google book preview). endobj The length of the shortest self-avoiding path connecting two distinct vertices u;v is called the graph distance between u and v, denoted by ˆ(u;v). Chen and L. Saloff-Coste, Comparison of cutoffs between lazy walks and Markovian semigroups, Journal of Applied Probability, vol. 17. ENEE 729p: Modern Discrete Probability. 50, no. 14 0 obj 153, no. We will cover the classic results and arguments of Percolation. 1, 1981, pp.1-12. Sebastien Roch, UW–Madison´ Modern Discrete Probability – Models and Questions. 9 0 obj Grading: Homeworks (30%), End of course presentation (40%), Take home exam (30%) The material covered here is considered in much greater depth in the follow-ing excellent texts. 12 0 obj Your presentation should be 17min long (this may change later depending on the number of groups) and prepared on slides. List of papers << /Length 11 0 R /Filter /FlateDecode >> 4, 2003, pp.671â687. 857-866. 16. endobj Inform. Fall 2019. 25, no.1-2, 2005, pp. << /Length 15 0 R /Filter /FlateDecode >> Barlow and E. A. Perkins, Symmetric Markov chains in $Z^d$: How fast can they move? Your goal is to enable your audience to take something home with them as a result of your presentation. 11 0 obj Graph terminology Basic examples of stochastic processes on graphs Exploring graphs Sebastien Roch, UW–Madison´ Modern Discrete Probability – … Presentation topics and materials will be distributed halfway into the course. 6 0 obj G.-Y. 5130-5140). The models include random graphs, Markov chains and mixing times, dynamics of graphical models, random matrices, as well as mathematical �v ���}�-�s�ehn�6B��}�tKnd�G�]��*���m�L}>t��Ӂ� A�P�B���� ��R�5]~]�>V'�Y��Qv`- �P}� Exposure to mathematical reasoning, particularly linear algebra and analysis. E. Lubetzky and A. Sly, Cutoff phenomena for random walks on random regular graphs, https://arxiv.org/abs/0812.0060 (Duke Matehmatical Journal, vol. Random walks and Markov chains. 1, 1990, pp.115-130. Course description: This is a graduate-level introduction to probabilistic reasoning for discrete systems. Preliminaries Some fundamental models Review of … 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. 1. Office hours Tuesday 11:00-12:00 or by arrangement. 194-203. N. Alon and M. Krivelevich. in the papers by Rolski et al.,5 Klugman et al.,6 Gajek7 or Gajek and Rudź8 among many others. … M.T. Probability Distribution of discrete random variable is the list of values of different outcomes and their respective probabilities. K. Marton, Bounding d-distance by information divergence, The Annals of Probability, vol.24, 1996, pp. 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. Probability Distribution of Discrete and Continuous Random Variable. D. Aldous and P. Diaconis, Shuffling cards and stopping times, The American Mathematical Monthly, vol. N. Madras and D. Randall, Factoring graphs to bound mixing rates, Prov. x���N�0E����L$0����G7H 2, 1988, pp. endobj We will have two dates for presentation: Friday Dec. 6 and Tuesday Dec. 10 (time and place are given in the shared Excel sheet). 3, 1997, pp.303â313. 475-810. 2. << /Length 5 0 R /Filter /FlateDecode >> endobj 3, 2010, pp. Your task is to present a problem and explain a solution, summarizing the main steps of the proof. << /ProcSet [ /PDF /Text ] /Font << /Ty2 8 0 R /Ty1 7 0 R >> >> 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. 4 Citations; 4 Mentions; 71k Downloads; Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 78) Log in to check access. Student presentations1. x�Zْ�F}�Wt��wԋ�. Generating random spanning trees more quickly than the cover time, Proc.
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