# Probability, Ergodic Theory, Mathematical Physics Seminar

## Exact Asymptotic Speed of a Traveling Wave with Large Noise

Carl Mueller, Rochester

Friday, April 26th, 2019
3:00 PM - 4:00 PM
Hylan 1106A

This is joint work with Leonid Mytnik and Lenya Ryzhik.

Traveling waves are a widespread phenomenon in physical systems. The Fisher-Kolmogorov-Petrovskii-Piscuinov (FKPP) equation is one of the simplest equations exhibiting traveling waves. Since physical systems often experience random disturbances, there is interest in the study of traveling waves in the presence of noise. We study solutions $u_t(x)$ to the following stochastic FKPP equation:

where $\dot{W}(t,x)$ is two-parameter white noise. Here $x\in\mathbf{R}$, and we assume that $u_0(x)=\mathbf{1}(x\leq0)$.

One can define the right hand edge $R(u_t)$ of the solution, and we consider the speed

There has already been work on the asymptotics of $V(\sigma)$ for $\sigma$ near 0. For large $\sigma$, Conlon and Doering gave the lower bound

We give a corresponding upper bound,

which shows that $\lim_{\sigma\to\infty}\sigma^2V(\sigma)=2$.

Event contact: arjun dot krishnan at rochester dot edu