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Integrable Systems and Random Matrix Theory Seminar

Stationary solutions for 1D Burgers equations and KPZ scaling
Monday, September 19, 2022
4:00-5:00 PM
ZOOM ID: 926 6491 9790 Off Campus Location
In the first part, we will talk about the stationary solutions for 1D stochastic Burgers equations and their ergodic properties. We will classify all the ergodic components, establish the "one force---one solution" principle, and obtain the inviscid limit. The key objects to study are the infinite geodesics and infinite-volume polymer measures in random environments, and the ergodic results have their counterparts in the geodesic/polymer language. In the second part, we will present a random point field model that is motivated by the coalescing and monotone structure of the optimal paths in random environments that arise in many KPZ models. The 2/3 transversal exponent from the KPZ scaling becomes a natural parameter for the renormalization action in this model, and can be potentially extended to values other than 2/3. Some preliminary results are given. Speaker(s): Liying Li (University of Michigan)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics