LAUSR

Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model

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1 Published in 2019 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-019-03643-w

Abstract: In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by… read more here.

Keywords: vertex model; limit; stochastic six; six vertex ... See more keywords

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

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1 Published in 2020 at "Probability Theory and Related Fields"

DOI: 10.1007/s00440-020-00966-x

Abstract: In this paper we consider the Higher Spin Six Vertex Model on the lattice $${\mathbb {Z}}_{\ge 2} \times {\mathbb {Z}}_{\ge 1}$$ . We first identify a family of translation invariant measures and subsequently we study… read more here.

Keywords: spin six; vertex model; model; higher spin ... See more keywords

Six-vertex model and Schramm-Loewner evolution.

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0 Published in 2017 at "Physical Review E"

DOI: 10.1103/physreve.95.052146

Abstract: Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a… read more here.

Keywords: schramm loewner; vertex model; ice; six vertex ... See more keywords

Current fluctuations of the stationary ASEP and six-vertex model

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1 Published in 2018 at "Duke Mathematical Journal"

DOI: 10.1215/00127094-2017-0029

Abstract: Our results in this paper are two-fold. First, we consider current fluctuations of the stationary asymmetric simple exclusion process (ASEP), run for some long time $T$, and show that they are of order $T^{1 /… read more here.

Keywords: stationary asep; vertex model; current fluctuations; six vertex ... See more keywords