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作者：Duminil-Copin, Hugo; Ioffe, Dmitry; Velenik, Yvan
作者单位：University of Geneva; Technion Israel Institute of Technology
摘要：We consider translationally-invariant percolation models on Z(d) satisfying the finite energy and the FKG properties. We provide explicit upper bounds on the probability of having two distinct clusters going from the end-points of an edge to distance n (this corresponds to a finite size version of the celebrated Burton-Keane [Comm. Math. Phys. 121 (1989) 501-505] argument proving uniqueness of the infinite-cluster). The proof is based on the generalization of a reverse Poincare inequality prov...
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作者：Miller, Jason; Watson, Samuel S.; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Microsoft
摘要：The conformal loop ensemble CLE kappa with parameter 8/3 < kappa < 8 is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given kappa and nu, we compute the almost-sure Hausdorff dimension of the set of points z for which the number of CLE loops surrounding the disk of radius epsilon centered at z has asymptotic growth nu log(1/epsilon) as epsilon -> 0. By extending these results to a setting in which the loops are ...
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作者：Ghosh, Subhroshekhar; Krishnapur, Manjunath; Peres, Yuval
作者单位：Princeton University; Indian Institute of Science (IISC) - Bangalore; Microsoft
摘要：We study continuum percolation on certain negatively dependent point processes on R-2. Specifically, we study the Ginibre ensemble and the planar Gaussian zero process, which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion. For the Ginibre ensemble, we establish the uniqueness of infinite cluster in the supercritical phase. For the Gaussian zero process, we establish that a non-trivial critical radius exists, and we prove the uni...
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作者：Bertoin, Jean
作者单位：University of Zurich
摘要：A new class of fragmentation-type random processes is introduced, in which, roughly speaking, the accumulation of small dislocations which would instantaneously shatter the mass into dust, is compensated by an adequate dilation of the components. An important feature of these compensated fragmentations is that the dislocation measure nu which governs their evolutions has only to fulfill the integral condition integral P(1 - p(1))(2)nu(dp) < infinity, where p = (p(1),...) denotes a generic mass...
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作者：Friz, Peter K.; Gess, Benjamin; Gulisashvili, Archil; Riedel, Sebastian
作者单位：Technical University of Berlin; Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Chicago; University System of Ohio; Ohio University
摘要：We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11(1983) 46-57]. This condition is verified in many examples, even in absence of explicit expressions for the covariance or Volterra kernels. Of special interest are random Fourier series, with covariance given as Fourier series itself, and we formulate conditions direct...
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作者：Guo, Xiaoqin
作者单位：Technical University of Munich
摘要：In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption that one of the following holds: (i) the environment is balanced and the perturbation satisfies a Kalikow-type ballisticity condition, (ii) the environment satisfies Sznitman's ballisticity condition. This is a generalized version of the Einstein relation for ...
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作者：Chevyrev, Ilya; Lyons, Terry
作者单位：University of Oxford; University of Oxford
摘要：We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue of the moment problem. We furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables. We apply our results to signature arising from Levy, Gaussian and Markov...
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作者：Kelly, David; Melbourne, Ian
作者单位：University of North Carolina; University of North Carolina Chapel Hill; New York University; University of Warwick
摘要：Consider an Ito process X satisfying the stochastic differential equation dX = a(X) dt + b(X) dW where a, b are smooth and W is a multidimensional Brownian motion. Suppose that W-n, has smooth sample paths and that Wn converges wealdy to W. A central question in stochastic analysis is to understand the limiting behavior of solutions X-n to the ordinary differential equation dX(n) = a(X-n) dt + b(X-n) dW(n). The classical Wong-Zakai theorem gives sufficient conditions under which X-n converges ...
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作者：Benoist, Yves; Quint, Jean-Francois
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a central limit theorem for random walks with finite variance on linear groups.
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作者：Fournier, Nicolas; Mischler, Stephane
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
摘要：We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials and Maxwell molecules. We establish a rate of propagation of chaos of the particle system to the unique solution of the Boltzmann equation. More precisely, we estimate the expectation of the squared Wasserstein distance with quadratic cost between the empirical measure of the particle system and the solution to the Boltzmann equation. The ...
