Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Supercritical behavior of asymmetric zero-range process with sitewise disorder

C. Bahadoran, T. Mountford, K. Ravishankar, and E. Saada

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 53, Number 2 (2017), 766-801.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments
Secondary: 82C22: Interacting particle systems [See also 60K35]

Zero-range process Site disorder Supercritical initial condition Large-time convergence Critical invariant measure Escape of mass Hydrodynamic limit


Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E. Supercritical behavior of asymmetric zero-range process with sitewise disorder. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 2, 766--801. doi:10.1214/15-AIHP736.

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