Phase transitions in the ASEP and stochastic six-vertex model
Name
1607.08684.pdf
Description
Submitted version
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900.16 KB
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Adobe PDF
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Author(s)
Aggarwal, Amol
Borodin, Alexei
Date Issued
March 2019
Journal
Annals of probability
Publisher
Institute of Mathematical Statistics
Citation
Aggarwal, Amol, and Borodin, Alexei. "Phase transitions in the ASEP and stochastic six-vertex model." Annals of Probability 47, 2 (2019): 613-689 © 2019 Institute of Mathematical Statistics
Version
Original manuscript
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. Keywords: asymmetric simple exclusion process, stochastic six-vertex model, Baik–Ben–Arous–Péché phase transition, stochastic higher spin vertex models, Kardar–Parisi–Zhang universality class
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1103/10.1214/17-aop1253
