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作者：Deijfen, Maria; Haggstrom, Olle
作者单位：Stockholm University; Chalmers University of Technology
摘要：The two-type Richardson model describes the growth of two competing infections on Z(d) and the main question is whether both infection types can simultaneously grow to occupy infinite parts of Z(d). For bounded initial configurations, this has been thoroughly studied. In this paper, an unbounded initial configuration consisting of points x = (x(1),center dot center dot center dot, x(d)) in the hyperplane H = {X epsilon Z(d) : x(1) = 0} is considered. It is shown that, starting from a configura...
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作者：Feng, Shui
作者单位：McMaster University
摘要：Several results of large deviations are obtained for distributions that are associated with the Poisson-Dirichlet distribution and the Ewens sampling formula when the parameter theta approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of theta going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of theta going to infinity in a Poisson-Dirichlet distribution corresponds to a finite ...
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作者：Birkner, Matthias; Depperschmidt, Andrei
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We study a discrete time spatial branching system on Z(d) With log iStic- type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with positive probability if the competition term is small enough. For a restricted set of parameter values, we also obtain uniqueness of the nontrivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model. Along the way we c...
