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May 2017 Supercritical behavior of asymmetric zero-range process with sitewise disorder
C. Bahadoran, T. Mountford, K. Ravishankar, E. Saada
Ann. Inst. H. Poincaré Probab. Statist. 53(2): 766-801 (May 2017). DOI: 10.1214/15-AIHP736

Abstract

We establish necessary and sufficient conditions for weak convergence to the upper invariant measure for one-dimensional asymmetric nearest-neighbour zero-range processes with non-homogeneous jump rates. The class of “environments” considered is close to that considered by (Stochastic Process. Appl. 90 (2000) 67–81), while our class of processes is broader. We also give in arbitrary dimension a simpler proof of the result of (In Asymptotics: Particles, Processes and Inverse Problems (2007) 108–120 Inst. Math. Statist.) with weaker assumptions.

Nous établissons des conditions nécessaires et suffisantes de convergence faible vers la mesure invariante maximale pour le processus de zero-range asymétrique à plus proche voisin en dimension un, avec des taux de sauts inhomogènes. La classe d’« environnements » considérée est proche de celle considérée dans (Stochastic Process. Appl. 90 (2000) 67–81), mais la classe de processus concernée est plus large. Nous donnons également, en dimension quelconque, une preuve plus simple du résultat de (In Asymptotics: Particles, Processes and Inverse Problems (2007) 108–120 Inst. Math. Statist.) sous des hypothèses plus faibles.

Citation

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C. Bahadoran. T. Mountford. K. Ravishankar. E. Saada. "Supercritical behavior of asymmetric zero-range process with sitewise disorder." Ann. Inst. H. Poincaré Probab. Statist. 53 (2) 766 - 801, May 2017. https://doi.org/10.1214/15-AIHP736

Information

Received: 18 November 2014; Revised: 19 November 2015; Accepted: 13 December 2015; Published: May 2017
First available in Project Euclid: 11 April 2017

zbMATH: 1369.60065
MathSciNet: MR3634274
Digital Object Identifier: 10.1214/15-AIHP736

Subjects:
Primary: 60K35, 60K37
Secondary: 82C22

Rights: Copyright © 2017 Institut Henri Poincaré

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Vol.53 • No. 2 • May 2017
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