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ASEP(q,j) converges to the KPZ equation
TLDR
In this paper, Carinci, Giardina, Redig and Sasamoto showed that ASEP(q,j) converges to the Cole-Hopf solution to the KPZ equation under weak asymmetry scaling.Abstract:
We show that a generalized Asymmetric Exclusion Process called ASEP(q,j) introduced by Carinci, Giardina, Redig and Sasamoto converges to the Cole-Hopf solution to the KPZ equation under weak asymmetry scaling.read more
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The KPZ fixed point
TL;DR: An explicit Fredholm determinant formula for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition was derived by.
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Open ASEP in the Weakly Asymmetric Regime
Ivan Corwin,Hao Shen +1 more
TL;DR: In this paper, it was shown that the bounded interval ASEP height function converges to the KPZ equation on the unit interval with Neumann boundary conditions on both sides (different parameter for each side).
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The KPZ Limit of ASEP with Boundary
TL;DR: In this article, the Laplace transform of the one-point distribution for half-line KPZ was obtained, and this was used to prove the GOE Tracy-Widom long-time fluctuations.
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The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions
TL;DR: In this paper, the authors consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases and prove that the large scale fluctuations of the system are well approximated by the solution to the KPZ equation provided the microscopic interaction is weakly asymmetric.
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A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
TL;DR: In this paper, a multi-species version of ASEP(q,j) is introduced, where up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry 0
References
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Book
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TL;DR: In this paper, it was shown that the weakly asymmetric exclusion process converges to the Kardar-Parisi-Zhang equation with a random noise on the density current.
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Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
TL;DR: In this article, the authors consider the crossover behavior between the symmetric and asymmetric exclusion processes and obtain explicit formulas for the one-dimensional marginal distributions, which interpolate between a standard Gaussian distribution and the GUE Tracy-Widom distribution.
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