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On transient behaviour of a nearest-neighbour birth-death process on a lattice

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Boris L. Granovsky  and
Liat Rozov
Boris L. Granovsky
Affiliation:
Technion — Israel Institute of Technology
Liat Rozov*
Affiliation:
Technion — Israel Institute of Technology
*
∗ Postal address for both authors: Department of Mathematics, Technion, Haifa, 32000, Israel.
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Abstract

We provide the explicit expression for the mean coverage function of a generalized voter model on a regular lattice and establish a characterization of the class of the above processes. As a result, we derive the exact rate of convergence of the considered processes to the steady state. We also prove the existence of different processes with the same mean coverage function on a given lattice.

Keywords

NEAREST-NEIGHBOUR INTERACTING PARTICLE SYSTEMSMEAN COVERAGE FUNCTIONRATE OF EXPONENTIONAL CONVERGENCE

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 549 - 553
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Financial support from the Fund for the Promotion of Research at Technion to the first author is gratefully acknowledged.

References

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