209, no. Inform. /Rotate 0 >> << /Length 15 0 R /Filter /FlateDecode >> 9 0 obj endstream 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. E. J. Candes, J. Romberg, and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. Spin systems and random constraint satisfaction problems. We will cover several foundational models 153, no. ENEE 729p: Modern Discrete Probability. Database-friendly random projections: Johnson-Lindenstrauss with binary coins, Journal of Computer and System Sciences, vol.66, no. 4, 2013, pp. Sebastien Roch, UW–Madison´ Modern Discrete Probability – Models and Questions. Rigorous location of phase transitions in hard optimization problems, Nature, vol.435, 2005, pp.759â764. 4, 2003, pp.671â687. D. Aldous and B. Flannery, Two applications of urn processes, Probability in the Engineering and Informational Sciences, vol. 3, 1972, pp.328-345. Deﬁnition A directed graph (or digraph for short) is a pair G = (V;E) where V is a set of vertices (or nodes, sites) and E V2is a set of directed edges. List of papers %��������� 4. 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. Room 405 Fine Hall. on Foundations of Computer Science, 1996, pp. << /Length 5 0 R /Filter /FlateDecode >> Barlow and E. A. Perkins, Symmetric Markov chains in $Z^d$: How fast can they move? 9. D. Achlioptas, A. Naor, and Y. Peres. 8, no. Modern Discrete Probability VI - Spectral Techniques Background Sebastien Roch´ UW–Madison Mathematics December 1, 2014 Sebastien Roch, UW–Madison´ Modern Discrete Probability – Spectral Techniques. << /Type /Page /Parent 3 0 R /Resources 12 0 R /Contents 10 0 R /MediaBox 943-959. M.T. 14. 8. The concepts will be recalled as needed in class.). 16, 2009, pp. 25, no.1-2, 2005, pp. Instructors : Alexander Barg, Ohad Elishco Department of Electrical and Computer Engineering/Institute for Systems Research Office: 2361 A.V.Williams Building. As you already know, a discrete probability distribution is specified by a probability mass function. S. Blackburn and S. Gerke, Connectivity of the uniform random intersection graphs, arXiv:0805.2814 (Discrete Mathematics, vol. 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. Some of the papers, cited in their final version, may be available on preprint servers such as arXiv. 7. 22. Topics covered are taken mostly from probability on graphs: percolation , random graphs , Markov random fields , random walks on graphs , etc. 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. Theory, vol. No attempt is made at covering these areas in depth. This paper offers a compact presentation of the solid involvement of Discrete Mathematics in various fields of Statistics and Probability Theory. 50, no. Solutions: | 1 | 2 | 3 |, [B17] P. Brémaud, Discrete Probability Models and Methods, Springer, 2017. Course Homepage: http://www.ece.umd.edu/~abarg/MDP. �XT,��RC�N@�'!~�iBBE�؞;s��l0�ԝ�q$�Ux@�s��dqm��+�8IB�F$9� Office: 2361 A.V.Williams Building. Looking at this table we can see that the greatest probability is \(P\begin{pmatrix}X = 6 \end{pmatrix} = \frac{36}{90}\). It's OK if you suggest a paper of your choice, but please receive instructor's approval in advance. Instructor availability outside class hours: Please approach us after class, and we will stay as long as needed to clear the questions. Class times: endobj Your goal is to enable your audience to take something home with them as a result of your presentation. Instructors : Alexander Barg, Ohad Elishco Fall 2019. We will cover the classic results and arguments of Percolation. 16. Lectures: Monday, Wednesday 12:30 - 1:45pm, AJC2121 333â348. 13. The above model can be found e.g. … P. Diaconis and L. Saloff-Coste, Logarithmic Soboloev inequalities for finite Markov chains, The Annals of Applied Probability, 1996, vol.6, no. 4. Discrete Probability Distributions, Essentials of Modern Business Statistics - David R. Anderson, Dennis J. Sweeney,Thomas A. Williams | All the textbook answe… L. Shepp, Covering the circle with random arcs, Israel Journal of Mathematics, vol.11, no. E-mails: abarg at umd dot edu and elishco at gmail dot com Probability Theory and Related Fields, vol. Your presentation should be 17min long (this may change later depending on the number of groups) and prepared on slides. The material covered here is considered in much greater depth in the follow-ing excellent texts. 17. 19. 6 0 obj D. Achlioptas. Instructors : Alexander Barg, Ohad Elishco Department of Electrical and Computer Engineering/Institute for Systems Research Office: 2361 A.V.Williams Building. Generating random spanning trees more quickly than the cover time, Proc. Probability Distribution of Discrete and Continuous Random Variable. 10. [0 0 612 792] /Rotate 0 >> 95--108. The goal of these notes is to give an introduction to fundamental models and techniques in graduate-level modern discrete probability. The class will focus on specific systems, and one of the central topics will be threshold behavior. 2 0 obj This function maps every element of a random variable’s sample space to a real number in the interval [0, 1].

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