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

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

2005-11-11

arxiv.org/abs/math/0511287v4

Annals of Probability 2007, Vol. 35, No. 4, 1201-1249

Mathematics

Probability

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

Scientific paper

10.1214/009117906000000971

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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