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作者：Hug, D; Reitzner, M; Schneider, R
作者单位：University of Freiburg; Technische Universitat Wien
摘要：In the early 1940s, D. G. Kendall conjectured that the shape of the zero cell of the random tessellation generated by a stationary and isotropic Poisson line process in the plane tends to circularity given that the area of the zero cell tends to infinity. A proof was given by I. N. Kovalenko in 1997. This paper generalizes Kovalenko's result in two directions: to higher dimensions and to not necessarily isotropic stationary Poisson hyperplane processes. In the anisotropic case, the asymptotic ...
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作者：Bahadoran, C
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider an arbitrary one-dimensional conservative particle system with finite-range interactions and finite site capacity, governed on the hydrodynamic scale by a scalar conservation law with Lipschitz-continuous flux h. A finite-size perturbation restricts the local current to some maximum value phi. We show that the perturbed hydrodynamic behavior is entirely determined by phi if inf(h; phi) is first nondecreasing and then nonincreasing, which we believe is a necessary condition.
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作者：Bardet, JB; Ben Arous, GR
作者单位：Universite Paris Nanterre; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider the (d + 1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on Z(d) together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this ...
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作者：Lawler, GF; Schramm, O; Werner, W
作者单位：Cornell University; Universite Paris Saclay; Microsoft
摘要：This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain D (subset of)(not equal) C is equal to the radial SLE2 path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that partial derivativeD is a C-1-simple closed curve, the same method is applied to show that the scaling limit of the uniform spanning tree Peano ...
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作者：Chang, CC; Landim, C; Lee, TY
作者单位：National Taiwan University; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a large deviations principle for the occupation time of a site in the two-dimensional symmetric simple exclusion process. The decay probability rate is of order t/logt and the rate function is given by Y-alpha(beta) = (pi/2){sin(-1)(2beta - 1) - sin(-1) (2alpha - 1))(2). The proof relies on a large deviations principle for the polar empirical measure which contains an interesting log scale spatial average. A contraction principle permits us to deduce the occupation time large deviatio...
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作者：Dalang, RC; Lévêque, O
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, which includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficient conditions on the spatial correlation of the noise for the existence (and uniqueness) of square-integrable solutions. In the particular case where the domain is a ball and the noise is concentrated on a sphere, we characterize the isotropi...
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作者：Cerrai, S; Röckner, M
作者单位：University of Florence; University of Bielefeld
摘要：Following classical work by Freidlin [Trans. Amer Math. Soc. (1988) 305 665-657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504-537] and Peszat [Probab. Theory Related Fields (1994) 98 113-136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction-diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results...
