Student Probability Seminar

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Intermediate Disorder Limits for Multi-Layer Random Polymers

Speaker: Mihai Nica

Location: Warren Weaver Hall

Date: Thursday, November 3, 2016, 2 p.m.

Synopsis:

Random polymers are disordered systems made from a random walk in a disordered environemtn. The intermediate disorder regime is a scaling limit for disordered systems where the inverse temperature is critically scaled to zero as the size of the system grows to infinity. For a random polymer given by a single random walk, Alberts, Khanin and Quastel proved that under intermediate disorder scaling the polymer partition function converges to the solution to the stochastic heat equation with multiplicative white noise. In this talk, I consider polymers made up of multiple non-intersecting walkers and consider the same type of limit. The limiting object now is the multi-layer extension of the stochastic heat equation introduced by O'Connell and Warren. This result proves a conjecture about the KPZ line ensemble.