ISSN:
1572-9230
Keywords:
Stochastic flow
;
infinite particle system
;
tightness
;
equilibrium
;
topological semigroup
;
random transformation
;
block charge model
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Consider a sequenceF 1,F 2,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM n(x), whereM n =F n ∘F n−1 ∘⋯∘F 1. We give conditions on the law ofF 1 for the sequence (M n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01046931
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