KPZ in equilibrium and directed polymers

Stochastics Seminar
Thursday, March 1, 2012 - 3:05pm
1 hour (actually 50 minutes)
Skyles 006
University of Wisconsin, department of Mathematics
The usual approach to KPZ is to study the scaling limit of particle systems. In this work, we show that the partition function of directed polymers (with a suitable boundary condition) converges, in a certain regime, to the Cole-Hopf solution of the KPZ equation in equilibrium. Coupled with some bounds on the fluctuations of directed polymers, this approach allows us to recover the cube root fluctuation bounds for KPZ in equilibrium. We also discuss some partial results for more general initial conditions.