PHASE TRANSITIONS IN THE ASEP AND STOCHASTIC SIX-VERTEX MODEL

• 成果类型: Article
• 署名作者: Aggarwal, Amol; Borodin, Alexei
• 署名单位: Harvard University; Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1253
• 发表日期: 2019
• 页码: 613-689
• 关键词: current fluctuations; LARGEST EIGENVALUE; free-energy; distributions; formulas; GROWTH; REPRESENTATION; asymptotics; tasep

摘要

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-Peche 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.