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作者：Cranston, M; Scheutzow, M; Steinsaltz, D
作者单位：University of Rochester; Technical University of Berlin
摘要：It has been suggested that stochastic flows might be used to model the spread of passive tracers in a turbulent fluid. We define a stochastic flow by the equations phi (0)(x) = x, d phi (t)(x) = F(dt, phi (t)(x)), where F(t, x) is a field of semimartingales on x is an element of R-d for d greater than or equal to 2 whose local characteristics are bounded and Lipschitz. The particles are points in a bounded set X, and we ask how far the substance has spread in a time T. That is, we define Phi (...
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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：Soshnikov, A
作者单位：California Institute of Technology; University of California System; University of California Davis
摘要：We discuss the CLT for the global and local linear statistics of random matrices from classical compact groups. The main parts of our proofs are certain combinatorial identities, much in the spirit of works by M. Kac and H. Spohn.
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作者：Cox, JT; Geiger, J
作者单位：Syracuse University; Goethe University Frankfurt
摘要：The genealogy of a cluster in the multitype voter model can be defined in terms of a family of dual coalescing random walks. We represent the genealogy of a cluster as a point process in a size-time plane and show that in high dimensions the genealogy of the cluster at the origin has a weak Poisson limit. The limiting point process is the same as for the genealogy of the size-biased Galton-Watson tree. Moreover, our results show that the branching mechanism and the spatial effects of the voter...
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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：Nualart, D; Viens, F
作者单位：University of Barcelona; University of North Texas System; University of North Texas Denton
摘要：We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup, whose kernel p(s, t, y, x) is Brownian in s and t. The kernel p is supposed to be measurable with respect to the increments of an underlying Wiener process in the interval [s, t]. The evolution equation is then anticipative and, choosing the Skorohod formulation, we establish existence and uniqueness of a continuous solution with values in L-2(R-d). As an ap...
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作者：Puha, AL
作者单位：California State University System; California State University San Marcos
摘要：The uniform model is a reversible interacting particle system that evolves on the homogeneous tree. Occupied sites become vacant at rate one provided the number of occupied neighbors does not exceed one. Vacant sites become occupied at rate beta times the number of occupied neighbors. On the binary tree, it has been shown that the survival threshold beta(c) is 1/4. In particular, for beta less than or equal to 1/4, the expected extinction time is finite. Otherwise, the uniform model survives l...
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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.
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作者：Verzani, J; Adler, R
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
摘要：We construct a super iterated Brownian motion (SIBM) from a historical version of iterated Brownian motion (IBM) using an iterated Brownian snake (IBS). It is shown that the range of super iterated Brownian motion is qualitatively quite different from that of super Brownian motion in that there are points with explosions in the branching. However, at a fixed time the support of SIBM has an exact Hausdorff measure function that is the same (up to a constant) as that of super Brownian motion at ...
