On diffusivity of a tagged particle in asymmetric zero-range dynamics
Sunder Sethuraman (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Sunder Sethuraman (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Alexei Borodin, Maurice Duits (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE...
Pablo A. Ferrari, Patricia Gonçalves, James B. Martin (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate ∈(1/2, 1] and to the left at rate 1−, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose...
Márton Balázs (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Penrose, Mathew D. (2008)
Probability Surveys [electronic only]
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Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude 1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type...