Limiting Current Distribution for a Two Species Asymmetric Exclusion Process

Chen, Zeying; Gier, Jan de; Hiki, Iori; Sasamoto, Tomohiro; Usui, Mikio

doi:10.1007/s00220-022-04408-8

Cited by 4 publications

(3 citation statements)

References 90 publications

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“…[545,[567][568][569]. Exact integral formulas were obtained for time-dependent microscopic probabilities [570][571][572][573][574], and GUE Tracy-Widom distributions were found for current fluctuations [575,576], in agreement with the predictions [577] from non-linear fluctuating hydrodynamics for the KPZ modes. for TASEP with two types of particles corresponding to the configuration of the system shown at the bottom.…”

Section: Several Conserved Quantitiessupporting

confidence: 67%

Riemann surfaces for KPZ with periodic boundaries

Prolhac

2020

SciPost Phys.

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The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to onedimensional KPZ universality in finite volume. Known exact results for fluctuations of the KPZ height with periodic boundaries are expressed in terms of meromorphic functions on this Riemann surface, summed over all the sheets of a covering map to an infinite cylinder. Connections to stationary large deviations, particle-hole excitations and KdV solitons are discussed.

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Section: Several Conserved Quantitiessupporting

confidence: 67%

Riemann surfaces for KPZ with periodic boundaries

Prolhac

2020

SciPost Phys.

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Section: Several Conserved Quantitiessupporting

confidence: 67%

KPZ fluctuations in finite volume

Prolhac

2024

SciPost Phys. Lect. Notes

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These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

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“…The fluctuation exponent of n-ASEP was addressed in finite size scaling of the gap of its generator [6], and the Bethe ansatz for the 2-ASEP with open boundaries was considered in [80]. To our knowledge, full explicit limiting distributions for multi-species models have only been derived recently for the two-species Arndt-Heinzl-Rittenberg (AHR) model [23][24][25], or in cases where there is a relation to a single species model such as shift colour-position symmetry [11,14] and the coalescing random walk [47].…”

Section: Multi-species Exclusion Processesmentioning

confidence: 99%

Transition probability and total crossing events in the multi-species asymmetric exclusion process

Gier

Mead

Wheeler

2023

J. Phys. A: Math. Theor.

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We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process ($r$-ASEP) with underlying $U_q(\widehat{\mathfrak{sl}}_{r+1})$ symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on $\mathbb{Z}$ in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general $r$-ASEP we employ a vertex model approach within which the probability of total crossing can be derived from partial symmetrization of an explicit high rank rainbow partition function. In the case of $r$-TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of $r$ determinants. For $2$-TASEP we additionally derive convenient formulas for cumulative total crossing probabilities using Bernoulli-step initial conditions for particles of type 2 and type 1 respectively.

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Limiting Current Distribution for a Two Species Asymmetric Exclusion Process

Cited by 4 publications

References 90 publications

Riemann surfaces for KPZ with periodic boundaries

Riemann surfaces for KPZ with periodic boundaries

KPZ fluctuations in finite volume

Transition probability and total crossing events in the multi-species asymmetric exclusion process

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