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作者：Castell, F
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We prove a homogenization result for system of semilinear parabolic PDEs of the type partial derivative(t)u(epsilon) = (1)/(2)e(2V(x/epsilon)) div (e(-2V(x/epsilon)) a(x/epsilon)delu(epsilon)) + h(x,u(epsilon), delu(epsilon)). where V and a are random ergodic fields. We extend to the random case, results of Buck-dahn, Hu & Peng [4] for periodic structures. The same method involving stability results is applied. Our main tool is an L-p estimate for the gradient of the solution of the auxiliary ...
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作者：Wang, WM
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We further develop thr supersymmetric formalism initiated in [W1] (see also [SjW]). We obtain the optimal mean field bounds at the critical energy for Lyapunov exponents of random walks in random potentials in Z(d) at weak disorder. This extends some of the results in [W1].
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作者：Li, WV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let B-0, B-1, ... , B-n be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time tau (n), = inf {t > 0 : B-i (t) - b(i) = B-0 (t) for some 1 less than or equal to i less than or equal to n} where 0 < b(i) less than or equal to 1, 1 < i less than or equal to n. In particular, we have E tau (3) = infinity and E tau (5) < infinity. Various generalizations are also studied.
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作者：Dekking, FM; von der Wal, P
作者单位：Delft University of Technology
摘要：Branching cellular automata (BCA) are introduced as generalisations of fractal percolation by admitting neighbour dependence. We associate sequences of random sets with BCA's and study their convergence. In case of convergence we derive the Hausdorff dimension of the limit set and of its boundary. To accomplish the latter we proof that the boundary of a set generated by a BCA is again a set generated by a BCA.
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作者：Cancrini, N; Martinelli, F
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR); Sapienza University Rome; University of L'Aquila; Roma Tre University
摘要：We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on Z(d) at inverse temperature beta. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any beta, with probability one, the spectral gap of the generator of the dynamics in a box of side L centered at the origin scales like L-2. Such an estimate is then used to prove a decay to equilibrium fo...
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作者：Artstein, Z
作者单位：Weizmann Institute of Science; Universite de Montpellier
摘要：The collection of sub-sigma -fields of a Borel measure space when endowed with the topology of strong convergence is in general not a compact space. The paper offers a completion of this space which makes it compact. The elements which are added to the space are called relaxed sigma -fields. A notion of relaxed conditional expectation with respect to it relaxed sigma -field is identified. The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional ...
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作者：Léandre, R
作者单位：Universite de Lorraine
摘要：We define a stochastic cohomology theory related to a stochastic diffeology for the Hoelder loop space. We show that the stochastic de Rham cohomology groups are equal to the deterministic de Rham cohomology groups of the Hoelder loop space. As an application, we show that a stochastic line bundle over the Brownian bridge (with fiber almost surely defined) is isomorphic to a true line bundle over the Hoelder loop space.
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作者：Greven, A; Klenke, A; Wakolbinger, A
作者单位：University of Erlangen Nuremberg; Goethe University Frankfurt
摘要：We study the longtime behaviour of interacting systems in a randomly fluctuating (space-time) medium and focus on models from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and interacting Fisher-Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is proportional to a random environment (catalytic medium). Here we introduce a model of interacting Fisher-Wright diffusions where...
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作者：Coffman, EG Jr; Lueker, GS; Spencer, J; Winkler, PM
作者单位：Columbia University; University of California System; University of California Irvine; New York University; Alcatel-Lucent; Lucent Technologies; AT&T
摘要：A random rectangle is the product of two independent random intervals, each being the interval between two random points drawn independently and uniformly from [0, 1]. We prove that the number C-n of items in a maximum cardinality disjoint subset of n random rectangles satisfies n(1/2)/K less than or equal to ECn less than or equal to Kn(1/2,) where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that,...
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作者：Burdzy, K; Le Gall, JF
作者单位：University of Washington; University of Washington Seattle; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider super-Brownian motion whose historical paths reflect from each other. unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any gamma > 0, a typical increment of a reflecting historical path over a...
