Seminar on Stochastic Processes 2004

Main Lectures in Math Annex 1100.

Afternoon sessions will be located in a subset of Math 104,105, LSK 200, LSK 460, LSK 462.
The Math Building is just across the road from the Mathematics Annex.

Coffee Breaks are in Math Annex 1115, just down the hall from the main lectures.

Sage Bistro is on campus, a short walk away from the Gage Residence.

Thursday

8:45-9:30	Registration and Coffee (Math Annex 1115)
9:30-10:30	Balint Virag, U. of Toronto Title: Zeros of i.i.d. Gaussian power series Abstract: A power series is Gaussian if its coefficients are jointly complex Gaussian random varaibles. We will review some recent developments concerning the geomteric properties of zeros of Gaussian power series. We will show that the zeros of the i.i.d. series form a determinantal process just like the eigenvalues of random matrices. We will present new results on the distribution of zeros and study the repulsion between them via a conformally invariant process. Joint work with Yuval Peres.
10:30-11:15	Coffee.
11:15-12:15	Rene Carmona, Princeton. U. Title: Pricing American Exercises
2:15-3:30	Two Parallel sessions of 15 min. presentations--scheduled from sign-up sheets.
3:30-4:00	Coffee
4:00-5:15	Single informal session with primary focus on short presentations of open problems (Math Annex 1100).

Friday

9:30-10:30	Robert Dalang, U. Lausanne Title: Recent results on the stochastic wave equation Abstract: The stochastic wave equation presents interesting challenges that are not present in the study of the stochastic heat equation. For instance, the kernel does not have a strong regularizing property and its irregularity increases with the dimension.We shall discuss issues of existence of solutions for linear and non-linear forms of the equation with various kinds of driving noises, some potential-theoretic results and, for spatial dimensions 2 and 3, some H\"older-Sobolev regularity estimates.
10:30-11:15	Coffee.
11:15-12:15	Yves Le Jan, U. Paris, Orsay. Title: Between coalescence and diffusion Abstract: Starting with an explicit discrete model of independent transition matrices, we obtain by renormalisation a class of continuous flows with independent increments which cannot be represented by a Brownian or Poissonian SDE. The possible extensions of this result to the general context of stochastic flows, associated with consistent systems of n-points Markov processes, will be also discussed.
2:15-3:30	Two Parallel sessions of 15 min. presentations--scheduled from sign-up sheets.
3:30-4:00	Coffee
4:00-5:15	Parallel informal sessions.
6:00-7:00	Reception at Sage Bistro. All are invited. Cash Bar.
7:00-	Banquet at Sage Bistro. Tickets $40 must be purchased at registration.

Saturday

9:30-10:30	Alice Guionnet, ENS Lyon Title: Asymptotics of spherical integrals and matrix models Abstract: In this talk, we shall describe the physics and combinatorial motivation to study matrix models and how it is related with the asymptotics of spherical integrals. We shall then discuss the asymptotics of these integrals as the size of the matrices go to infinity, and deduce the first order asymptotics of some matrix models such as the Ising model on random graphs as well as the dually weighted graph model. (joint work with O.Zeitouni and M.Maida)
10:30-11:00	Coffee.
11:00-12:00	Final informal session in Math Annex 1100.