Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume

Kirone Mallick (1) , Sylvain Prolhac (2, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 PhyStat - Physique Statistique des Systèmes Complexes (LPT)
3 LPT - Laboratoire de Physique Théorique

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.

Mots clés: TASEP; KPZ fluctuations; finite volume; non-intersecting Brownian bridges

Domaines: Mécanique statistique [cond-mat.stat-mech]

Kirone Mallick, Sylvain Prolhac. Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume. Journal of Statistical Physics, 2018, 173 (2), pp.322-361. ⟨10.1007/s10955-018-2136-4⟩. ⟨hal-01915293⟩