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July 2007 Existence of the zero range process and a deposition model with superlinear growth rates
M. Balázs, F. Rassoul-Agha, T. Seppäläinen, S. Sethuraman
Ann. Probab. 35(4): 1201-1249 (July 2007). DOI: 10.1214/009117906000000971

Abstract

We give a construction of the zero range and bricklayers’ processes in the totally asymmetric, attractive case. The novelty is that we allow jump rates to grow exponentially. Earlier constructions have permitted at most linearly growing rates. We also show the invariance and extremality of a natural family of i.i.d. product measures indexed by particle density. Extremality is proved with an approach that is simpler than existing ergodicity proofs.

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M. Balázs. F. Rassoul-Agha. T. Seppäläinen. S. Sethuraman. "Existence of the zero range process and a deposition model with superlinear growth rates." Ann. Probab. 35 (4) 1201 - 1249, July 2007. https://doi.org/10.1214/009117906000000971

Information

Published: July 2007
First available in Project Euclid: 8 June 2007

zbMATH: 1138.60340
MathSciNet: MR2330972
Digital Object Identifier: 10.1214/009117906000000971

Subjects:
Primary: 60K35
Secondary: 82C41

Keywords: bricklayer’s , construction of dynamics , ergodicity of dynamics , superlinear jump rates , Zero range

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 4 • July 2007
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