Abstract
The purpose of this chapter is to give an introduction to interacting particle systems by describing the behavior of several examples. In each system there is a collection of spatial locations called sites, which in all our examples will be the d-dimensional integer lattice, Z d, that is, the points in d-dimensional space with all integer coordinates. At each time t ∈ [0, ∞), each site can be in one of a finite set of states, F, so the state of the process at time t is a. function ξ t : Z d → F. The time evolution is described by declaring that each site changes its state at a rate that depends upon the states of a finite number of neighboring sites. Here, we say that something happens at rate r if the probability of an occurrence between times t and t + h is ~ rh as h → 0 is small; that is, when divided by h, the probability converges to r as h → 0.
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© 1993 Springer-Verlag Berlin Heidelberg
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Durrett, R. (1993). Stochastic Models of Growth and Competition. In: Levin, S.A., Powell, T.M., Steele, J.W. (eds) Patch Dynamics. Lecture Notes in Biomathematics, vol 96. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50155-5_13
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DOI: https://doi.org/10.1007/978-3-642-50155-5_13
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