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Probability and Computational Finance Seminar
Zhipeng Liu
Courant Institute of Mathematical Sciences, New York University
Title: TASEP on a ring in relaxation time scale

Abstract: Gaussian fluctuation has been known as a universal law behind many mathematical physics models: quantities that are a large sum of i.i.d. random variables converge to Gaussian distribution, which is independent of the distribution of individual random variables. Recently a theory on a new universality class, the so-called KPZ universality class, has been rapidly developed. In this universality class, the one point distributions are expected to be universal and independent of the model, but only depend on the initial data. 

In this talk, we consider a specific model which lies in the crossover between KPZ and Gaussian universality classes: the totally asymmetric simple exclusion process (TASEP) on a ring. It has been conjectured since the 80's that the system starts to relax when time is 3/2 power of the system size. Before the relaxation time scale, the system belongs to KPZ universality class and the limiting distribution depends on the initial data. And after the relaxation time scale, the system reaches equilibrium and the limiting distribution is Gaussian. We will show the crossover distributions in the relaxation time scale for three classical initial conditions. These crossover distributions interpolate the distributions in KPZ universality classes and the Gaussian distribution, and are expected to be universal for any periodic system in KPZ universality class.

Date: Monday, March 20, 2017
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve