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March 2019 Phase transitions in the ASEP and stochastic six-vertex model
Amol Aggarwal, Alexei Borodin
Ann. Probab. 47(2): 613-689 (March 2019). DOI: 10.1214/17-AOP1253

Abstract

In this paper, we consider two models in the Kardar–Parisi–Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call shape generalized step Bernoulli initial data) for both of these models that generalizes the step Bernoulli initial data studied in a number of recent works on the ASEP. Under this class of initial data, we analyze the current fluctuations of both the ASEP and stochastic six-vertex model and establish the existence of a phase transition along a characteristic line, across which the fluctuation exponent changes from $1/2$ to $1/3$. On the characteristic line, the current fluctuations converge to the general (rank $k$) Baik–Ben–Arous–Péché distribution for the law of the largest eigenvalue of a critically spiked covariance matrix. For $k=1$, this was established for the ASEP by Tracy and Widom; for $k>1$ (and also $k=1$, for the stochastic six-vertex model), the appearance of these distributions in both models is new.

Citation

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Amol Aggarwal. Alexei Borodin. "Phase transitions in the ASEP and stochastic six-vertex model." Ann. Probab. 47 (2) 613 - 689, March 2019. https://doi.org/10.1214/17-AOP1253

Information

Received: 1 August 2016; Revised: 1 September 2017; Published: March 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07053553
MathSciNet: MR3916931
Digital Object Identifier: 10.1214/17-AOP1253

Subjects:
Primary: 60K35, 82C22

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 2 • March 2019
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