The Annals of Probability

Existence of the zero range process and a deposition model with superlinear growth rates

M. Balázs, F. Rassoul-Agha, T. Seppäläinen, and S. Sethuraman

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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.

Article information

Source
Ann. Probab., Volume 35, Number 4 (2007), 1201-1249.

Dates
First available in Project Euclid: 8 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1181334244

Digital Object Identifier
doi:10.1214/009117906000000971

Mathematical Reviews number (MathSciNet)
MR2330972

Zentralblatt MATH identifier
1138.60340

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

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

Citation

Balázs, M.; Rassoul-Agha, F.; Seppäläinen, T.; Sethuraman, S. Existence of the zero range process and a deposition model with superlinear growth rates. Ann. Probab. 35 (2007), no. 4, 1201--1249. doi:10.1214/009117906000000971. https://projecteuclid.org/euclid.aop/1181334244


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