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

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.

Published at http://dx.doi.org/10.1214/009117906000000971 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Growth fluctuations in a class of deposition models
• Microscopic shape of shocks in a domain growth model
• Multiple shocks in bricklayers' model

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