Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs; Júlia Komjáthy; Timo Seppäläinen

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 1, page 151-187
  • ISSN: 0246-0203

Abstract

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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 t1/3. 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 processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors’ earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.

How to cite

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Balázs, Márton, Komjáthy, Júlia, and Seppäläinen, Timo. "Microscopic concavity and fluctuation bounds in a class of deposition processes." Annales de l'I.H.P. Probabilités et statistiques 48.1 (2012): 151-187. <http://eudml.org/doc/272024>.

@article{Balázs2012,
abstract = {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 t1/3. 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 processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors’ earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.},
author = {Balázs, Márton, Komjáthy, Júlia, Seppäläinen, Timo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting particle systems; universal fluctuation bounds; t1/3-scaling; second class particle; convexity; asymmetric simple exclusion; zero range process; scaling; KPZ model; microscopic concavity hypothesis; Tracy-Widom distributions and processes; determinantal representation},
language = {eng},
number = {1},
pages = {151-187},
publisher = {Gauthier-Villars},
title = {Microscopic concavity and fluctuation bounds in a class of deposition processes},
url = {http://eudml.org/doc/272024},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Balázs, Márton
AU - Komjáthy, Júlia
AU - Seppäläinen, Timo
TI - Microscopic concavity and fluctuation bounds in a class of deposition processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 1
SP - 151
EP - 187
AB - 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 t1/3. 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 processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors’ earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.
LA - eng
KW - interacting particle systems; universal fluctuation bounds; t1/3-scaling; second class particle; convexity; asymmetric simple exclusion; zero range process; scaling; KPZ model; microscopic concavity hypothesis; Tracy-Widom distributions and processes; determinantal representation
UR - http://eudml.org/doc/272024
ER -

References

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