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Boundary statistics for the six-vertex model with DWBC (2310.12735v1)

Published 19 Oct 2023 in math.PR, math-ph, math.CO, and math.MP

Abstract: We study the behavior of configurations in the symmetric six-vertex model with $a,b,c$ weights in the $n\times n$ square with Domain Wall Boundary Conditions as $n\to\infty$. We prove that when $\Delta=\frac{a2+b2-c2}{2ab}<1$, configurations near the boundary have fluctuations of order $n{1/2}$ and are asymptotically described by the GUE-corners process of the random matrix theory. On the other hand, when $\Delta>1$, the fluctuations are of finite order and configurations are asymptotically described by the stochastic six-vertex model in a quadrant. In the special case $c=0$ (which implies $\Delta>1$), the limit is expressed as the $q$-exchangeable random permutation of infinitely many letters, distributed according to the infinite Mallows measure.

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