## Phase transitions in the ASEP and stochastic six-vertex model.(English)Zbl 1466.60191

Summary: 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.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics
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