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SPDE limits of six-vertex model

Presented by: 
Hao Shen University of Wisconsin-Madison
Date: 
Thursday 13th December 2018 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
The theme of the talk is deriving stochastic PDE limits as description of large-scale fluctuations of the six-vertex (6V) model in various regimes. <br> We will consider two types of 6V model: stochastic 6V and symmetric 6V. <br> For stochastic 6V in a weakly asymmetric regime, under parabolic scaling the height function fluctuation converges to solution of KPZ equation after suitable re-centering and tilting. For symmetric 6V, in a regime where parameters are tuned into the ferroelectric/disordered phase critical point, under parabolic scaling the line density fluctuations in a one-parameter family of Gibbs states converge to solution of stationary stochastic Burgers. <br> Again for stochastic 6V, in a regime where the corner-shape vertex weights are tuned to zero, under hyperbolic scaling, the height fluctuation converges to the solution of stochastic telegraph equation. <br> We will discuss challenges and new techniques in the proofs.<br> Based on a joint work with Ivan Corwin, Promit Ghosal and Li-Cheng Tsai, and a joint work with Li-Cheng Tsai.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons