Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume

Abstract

Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium steady state depends on the initial condition. Using a reformulation of the matrix product representation for the dominant eigenstate, the statistics of the height at large scales is expressed, for arbitrary initial conditions, in terms of extremal values of independent standard Brownian bridges. Comparison with earlier exact Bethe ansatz asymptotics leads to explicit conjectures for some conditional probabilities of non-intersecting Brownian bridges with exponentially distributed distances between the endpoints.

43 pages, 5 figures

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Cited by in corpus (8)

• Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions
• Riemann surfaces for KPZ with periodic boundaries
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Riemann surface for TASEP with periodic boundaries
• KPZ fluctuations in finite volume
• Exact short-time height distribution and dynamical phase transition in the relaxation of a Kardar-Parisi-Zhang interface with random initial condition
• Approach to stationarity for the KPZ fixed point with boundaries
• Current fluctuations for the second class particle : joint statistics