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Probability Seminar List

Seminar List for Fall 2002

Oct 1, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker Irene Hueter, Baruch College
Title On the 3/4-Conjecture of the Self-Avoiding Walk
Abstract The self-avoiding walk (SAW) kept much of its fascination ever since the chemist Paul Flory called upon this model in 1948 when he observed that the end-to-end distance of a linear polymer chain in 3 dimensions must have a power of the chain length larger than 1/2 and should approach 0.6. Experiments and numerical work later confirmed this effect. If we walk through the gallery of open conjectures and speculations on the SAW, we find a major long-standing conjecture in the field which states that the SAW in the 2-dimensional integer lattice has expected distance exponent 3/4.

We will discuss background on the SAW and the weakly SAW, a related walk that allows but penalizes self-intersections. We will look at a stochastic process which suppresses self-intersections in a cone and for which the distance exponent 3/4 emerges, and explain how this exponent carries over to both, the weakly SAW and the SAW in the square lattice. Moreover, we will survey the 3-dimensional SAW and mention a number of open questions awaiting progress.

Oct 8, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker Michael Marcus, City College
Title Continuity of infinitely divisible processes via Poisson point processes.
Oct 15, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker John Verzani, CUNY/College of Staten Island
Title An example of an extreme X-harmonic function
Oct 29, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker Martin Hildebrand, State University of New York at Albany
Title Random Random Walks on Finite Groups and a Result of Erdös and Renyi
Abstract This talk will consider lazy "random random walks" on finite groups. To do so, one chooses a set of elements at random from the group, and then one performs a random walk where, at each step, one multiplies either by the identity element or by an element chosen at random from this set. Informally, questions one could examine would be to see if, for a specified size of the set of elements chosen at random, the typical random walk will become close to uniformly distributed on the group and, if so, how many steps does it take to do so. This talk will examine such questions asked more carefully and will describe some work of Erdös and Renyi, of Pak, and of the speaker.
Nov 5, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker Elena Kosygina, Baruch College
Title Long term behavior of a Brownian flow with jumps
Abstract We consider a stochastic jump flow in an interval (-a,b), a,b > 0. Each particle performs a canonical Brownian motion and jumps to zero when it reaches -a or b. We study the long term behavior of a random measure, which is a push-forward of a given finite initial measure on (-a,b) under this flow.
Nov 21, 2002 9:30am, Room Segal Theatre. First floor CUNY Graduate CenterEdit Delete B/W(color)Hard CopyEmail Entry
Speaker Shi, Burdzy, Bass and Foguel, Conference on Stochastic Processes
Title Conference on Stochastic Processes
Nov 22, 2002 9:30am, Room Segal Theatre. First floor CUNY Graduate CenterEdit Delete B/W(color)Hard CopyEmail Entry
Speaker Lawler and Li, Conference on Stochastic Processes (day 2)
Title Conference on Stochastic Processes (day 2)
Dec 10, 2002 4:00pm, Room 5417Edit Delete B/W(color)Hard CopyEmail Entry
Speaker Gérard Ben Arous, Courant Institute of Mathematical Sciences
Title Universality for Random Sample Covariance Matrices and Bessel Processes
Abstract We prove universality for the spectrum of random covariance matrices when the distribution of the i.i.d entries is "Gaussian -Divisible", i.e., any probability measure convoluted with a Gaussian. We obtain universality in the bulk and at the edges (soft and hard). The method of proof is based on an argument by K.Johansson for Wigner matrices, and the study of the natural matrix Brownian motion. This is a joint work with Sandrine Peche (EPFL, Lausanne).