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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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

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

First available in Project Euclid: 8 June 2007

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Zentralblatt MATH identifier

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]

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


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.

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