Branching exclusion process on a strip |
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Authors: | Fábio P Machado |
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Institution: | (1) Department of Statistics, Universidade de São Paulo, São Paulo, Brazil;(2) Department of Mathematics, Cornell University, Ithaca, New York |
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Abstract: | We consider a model of stochastically interacting particles on an infinite strip of 2; in this model, known as a branching exclusion process, particles jump to each empty neighboring site with rate /4 and also can create a new particle with rate 1/4 at each one of these sites. The initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied. We prove that this process has exactly one invariant measure with the property thatH, the number of empty sites to the left of the rightmost particle, has an exponential moment. This refines a result presented by Bramson {eaet al.}, who proved that ford=1,H is finite with probability 1. |
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Keywords: | Microscopic interface branching exclusion process invariant measure hitting time |
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