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<p>Interacting particle systems have been applied to model the spread of infectious
diseases and opinions, interactions between competing species, and evolution of forest
landscapes. In this thesis, we study three spatial models arising from from ecology
and social sciences. First, in a model introduced by Schelling in 1971, in which families
move if they have too many neighbors of the opposite type, we study the phase transition
between a randomly distributed and a segregated equilibrium. Second, we consider a
combination of the contact process and the voter model and study the asymptotics of
the critical value of the contact part as the rate of the voting term goes to infinity.
Third, we consider a family of attractive stochastic spatial models, one of which
is introduced by Staver and Levin to describe the coverage of forest. We prove that
the mean-field ODE gives the asymptotically sharp phase diagram for existence of stationary
distributions, while for Staver and Levin model there can still be non-trivial stationary
distributions even when the absorbing fixed point of the mean-field ODE is stable.</p>
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