Columbia-Princeton Probability Day 2012


Columbia University, March 2, 2012







Confirmed Speakers
  • J. C. Mattingly (Duke University)
  • R. Pemantle (University of Pennsylvania)
  • L. Saloff-Coste (Cornell University)
  • T. Seppäläinen (University of Wisconsin-Madison)
  • M. Damron (Princeton University)



Schedule

9:30-10:00
Registration/Breakfast
10:00-11:00
T. Seppäläinen [abstract]
11:00-12:00
J. C. Mattingly [abstract]
12noon-2:00
Lunch Break
2:00-3:00
R. Pemantle [abstract]
3:00-3:15 Coffee Break 
3:15-4:15 L. Saloff-Coste [abstract]
4:15-5:00 M. Damron [abstract]




Practical Information
The conference will take place in Columbia University's Northwest Corner Building Room 501, on March 2, 2012.

Directions to Columbia's Mornigside Heights Campus.

Please register in order to attend the conference. (Registration is free.)

For further information, please contact the organizers.




Titles and Abstracts


T. Seppäläinen (University of Wisconsin-Madison)
Exactly solvable directed polymers in the KPZ universality class

Abstract: Three exactly solvable 1+1 dimensional directed polymer models are currently known in the KPZ (Kardar-Parisi-Zhang) universality class: the KPZ equation itself, the O'Connell-Yor polymer in a Brownian environment, and the log-gamma polymer.  This talk begins with the general picture, contrasts the KPZ class with the EW (Edwards-Wilkinson) class, and then focuses on aspects of the exact solvability of the log-gamma polymer.


J. C. Mattingly (Duke University)
Hidden dissipation and Stochastic Stabilization:  Modest Examples

Abstract: I will talk about some simple low dimensional SDEs where difficulty in establishing a unique attracting stationary measure comes not form the uniqueness but from proving the stability needed to show existence of a stationary measure is some cases or that the dynamics is stable starting from any initial point in other cases. At the base, the solutions will be an exercise in constructing a stochastic Lyapunov function. We will make a concerted attempt to develop a rational construction which doesn't relay on inspired guesses but rather uses the structure of the underlying dynamics. In the process we will discover hidden asymptotic problems and make connections to averaging an homogenization theory.


R. Pemantle (University of Pennsylvania)
Negative depencence and concentration inequalities

Abstract. I will begin by introducing the Borcea-Branden-Ligget theory of negative dependence for binary random variables via stable polynomials.  Next I will show how it can be applied to produce concentration inequalities that generalize those for functionals of IID variables.


L. Saloff-Coste (Cornell University)
Random walks driven by low moment measures

Abstract: In the theory of random walks on groups, special attention is given to random walks driven by finitely supported symmetric measure. In particular, the basic behavior of the probability of return as a function of the number of steps can be viewed as a group invariant. In this talk, I will consider basic questions regarding  random walks driven by measures that have some finite low moment (here, "low" means lower than 2). Sharp lower bounds on the probability of return will be derived under minimal assumptions.


M. Damron (Princeton University)
The regeneration structure of 2d invasion percolation

Abstract. Invasion percolation is a stochastic growth model which
displays ``self-organized criticality.'' In other words, it does not
have a parameter but it mirrors aspects of a parametric model at
criticality. In this talk I will describe work with A. Sapozhnikov on
a renewal structure in invasion percolation and how
we exploit it to prove new limit theorems and variance estimates for
the model.