Speakers:
Charles Bordenave (Toulouse)Second speaker 5:10-6:00: Mykhaylo Shkolnikov (Berkeley)
Systems of diffusion processes (particles) with rank-based interactions have been studied heavily due to their importance in stochastic portfolio theory and the intriguing relations with particle systems appearing in statistical physics. We will study the behavior of this particle system as the number of particles gets large. By obtaining a large deviations principle, we will show that the limiting dynamics can be described by a porous medium equation with convection, whereas paths of finite rate are given by solutions of appropriately tilted versions of this equation. This is the first instance of a large deviations principle for diffusions interacting both through the drift and the diffusion coefficients with the diffusion coefficients not being globally Lipschitz (and not even continuous). Based on joint work with A. Dembo, S.R.S. Varadhan and O. Zeitouni.
Second speaker 5:10-6:00: Nike Sun (Stanford)
Satisfaction and optimization problems subject to random constraints are a well-studied area in the theory of computation. These problems also arise naturally in combinatorics, in the study of sparse random graphs. While the values of limiting thresholds have been conjectured for many such models, few have been rigorously established. In this context we study the size of maximum independent sets in random d-regular graphs. We show that for d exceeding a constant d(0), there exist explicit constants A, C depending on d such that the maximum size has constant fluctuations around A*n-C*(log n) establishing the one-step replica symmetry breaking heuristics developed by statistical physicists. As an application of our method we also prove an explicit satisfiability threshold in random regular k-NAE-SAT.
This is joint work with Jian Ding and Allan Sly.
Metric properties of random maps (graphs embedded in surfaces) have been subject to a lot of recent interest. In this talk, I will review a combinatorial approach to these questions, which exploits bijections between maps and some labeled trees. Thanks to an unexpected phenomenon of "discrete integrability", it is possible to enumerate exactly maps with two or three points at prescribed distances, and more. I will then discuss probabilistic applications to the study of the Brownian map (obtained as the scaling limit of random planar maps) and of uniform infinite planar maps (obtained as local limits). If
time allows, I will also explain the combinatorial origin of discrete integrability, related to the continued fraction expansion of the so-called resolvent of the one-matrix model. Based on joint works with E. Guitter and P. Di Francesco.
Speakers:
Mark Rudelson (Michigan)Semester/Year programs:
September - December 2012: Institute for Computational and Experimental Research in Mathematics Semester Program on Computational Challenges in Probability, Providence RI
April - September 2013: Lebesgue Center Semester Program on Perspectives in Analysis and Probability, Rennes France
September 2013 - June 2014: Institute for Advanced Studied Year Program on Non-equilibrium Dynamics and Random Matrices
Schools:May 27-31, 2013: IHP Spring School on Threshold phenomena and random graphs, Paris, France.
June 3-7, 2013: Lebesgue Center Summer School on KPZ Equation and Rough Paths, Rennes France
June 3-15, 2013: The Beg Rohu Summer School on Disordered Systems, Saint Pierre Quiberon, France
July 14-26, 2013: 9th Cornell Probability Summer School , Cornell
July, 2013: Fields Institute focus program on Noncommutative Distributions in Free Probability Theory , Toronto, Canada
August 4-10, 2013: 17th Brazilian School of Probability
August 5-19, 2013: Bielefeld University Summer School on Randomness in Physics and Mathematics
Conferences and Lecture Series:March 14-16, 2013: Seminar on Stochastic Processes, Duke
July 29, 2013 - August 2, 2013: Stochastic Processes and Applications, Boulder, CO
July 22-26, 2013: StatPhys 25, Seoul, Korea
August 19-23, 2013: Analysis of Stochastich Partial Differential Equations, Michigan State University
Probability seminars in past semesters:
Fall 2012 : Spring 2012 : Fall 2011 : Spring 2011 : Fall 2010 : Spring 2010 : Fall 2009 : Spring 2009 : Fall 2008