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Probability Seminar List

The CUNY Probability Seminar is typically held on Tuesdays at 4pm in the CUNY Graduate Math Department. The exact dates, times and locations are mentioned below.

Seminar List for Fall 2004

Oct 12, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker Jay Rosen, CUNY/CSI
Title Frequently visited sets for random walks
Oct 19, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker Irene Hueter, Baruch College
Title Random convex hulls and the Stein method
Abstract I will survey a few of the results and many open problems of the wide literature on the convex hull of a random point set in Rd. Random convex sets have a long mathematical history and commonly arise in linear programming algorithms, imaging and in multivariate statistics. I will explain how the Stein method can be applied to prove asymptotic normality of the number of vertices of a random convex hull and bound the normal approximation error.
Oct 26, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker Olivier Daviaud, Stanford, Morgan Stanley
Title Extremes of the discrete Gaussian free field in 2-d
Abstract The two dimensional Gaussian free field (on the square lattice {1,...,N}2) is a well-known Gaussian random surface. Its asymptotic maximum (for large N) was first computed by Bolthausen et al. (2001). Building on this work and drawing inspiration from Dembo et al. (2004), we exhibit an intricate multi-fractal structure for the sets where the field is unusually high (or low). Next, we show that this structure remains unchanged when the field is conditioned on being everywhere positive (phenomenon of entropic repulsion). Finally, in light of these results we propose a suggestive analogy between the square of the free field and the two-dimensional simple random walk on the discrete torus.
Nov 9, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker David Asher Levin, University of Utah
Title Dynamical Random Walks
Abstract A dynamical random walk is a stationary, path-valued process which at any fixed time has the same law on paths as a random walk. Benjamini, Haggstrom, Peres, and Steif (2003) first studied which almost-sure properties of random walk may fail to hold at (random) times for the dynamical version. I will describe some atypical behavior which occurs for dynamical random walks, and discuss the role played by the Kolmogorov entropy in analyzing exceptional sets.

This is joint work with Davar Khoshnevisan and Pedro Mendez.

Nov 16, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker Peter Mörters, University of Bath
Title Large deviations for Markov chains on random trees
Nov 23, 2004 4:00pm, Room 5417click for b/w(color) postscript file
Speaker Roger Mansuy , University of Paris
Title A Tanaka formula for the symmetric Levy processes