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Key words: Voter model, Lotka-Volterra model, spatial competition, stochastic partial differen- tial equations, long-range limits.. AMS 2000 Subject Classification: Primary
Key words: Spatial coagulation model; post-gelation behavior; stochastic particle systems AMS 2000 Subject Classification: Primary 60K40.. Submitted to EJP on June 2 2006, final
Recently, in [MR07c], we have shown that the edge-reinforced random walk on any locally finite graph has the same distribution as a random walk in a random environment given by
Key words: Parabolic Anderson model, catalytic random medium, exclusion process, Lya- punov exponents, intermittency, large deviations, graphical representation.. AMS 2000
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from
Key words: infinite divisibility, Lévy measure, O -subexponentiality, dominated variation, expo- nential class.. AMS 2000 Subject Classification: Primary 60E07;
A related model is the directed polymer in a random medium (DPRM), in which the underlying Markov chain is generally taken to be SSRW on Z d and the polymer encounters a
We also show that the emergence of giant cycles coincides with a phase transition in the acceleration of the random walk, as measured by the second derivative of the distance (on
