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作者：Dawson, DA; Fleischmann, K; Mueller, C
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Rochester
摘要：Consider a catalytic super-Brownian motion X = X-Gamma with finite variance branching. Here catalytic means that branching of the reactant X is only possible in the presence of some catalyst. Our intrinsic example of a catalyst is a stable random measure Gamma on R of index 0 < < 1. Consequently, here the catalyst is located in a countable dense subset of R. Starting with a finite reactant mass Xo supported by a compact set, X is shown to die in finite time. We also deal with two other cases, ...
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作者：Picard, J
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Harmonic maps are viewed as maps sending a fixed diffusion to manifold-valued martingales. Under a convexity condition, we prove that the continuity of real-valued harmonic functions implies the continuity of harmonic maps. Then we prove with a probabilistic method that continuous harmonic maps are smooth under Hormander's condition; the proof relies on the study of martingales with values in the tangent bundle.
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作者：Stannat, W
作者单位：University of Bielefeld
摘要：We prove that Fleming-Viot operators with parent-independent mutation satisfy a logarithmic Sobolev inequality if and only if the set of types is finite.
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作者：Talagrand, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; University System of Ohio; Ohio State University
摘要：Gardner and Derrida have introduced a natural version of the problem of the capacity of the binary perceptron with temperature, and they proposed (based on physical methods) remarkable formulas for this model. We give a complete rigorous proof that these formulas are correct at sufficiently high temperature for a much larger class of models.
