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作者：Neel, Robert W.; Popescu, Ionel
作者单位：Lehigh University; University System of Georgia; Georgia Institute of Technology; Romanian Academy; Institute of Mathematics of the Romanian Academy
摘要：We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this stochastic approach, we give a proof that, for surfaces of nonpositive Euler characteristic, the normalized Ricci flow converges to a constant curvature metric exponentially quic...
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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13
摘要：We are interested in the randomly biased random walk on the supercritical Galton-Watson tree. Our attention is focused on a slow regime when the biased random walk (X-n) is null recurrent, making a maximal displacement of order of magnitude (log n)(3) in the first n steps. We study the localization problem of X-n and prove that the quenched law of X-n can be approximated by a certain invariant probability depending on n and the random environment. As a consequence, we establish that upon the s...
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作者：Saloff-Coste, Laurent; Zheng, Tianyi
作者单位：Cornell University; Stanford University
摘要：Let G be a finitely generated group equipped with a finite symmetric generating set and the associated word length function vertical bar center dot vertical bar. We study the behavior of the probability of return for random walks driven by symmetric measures cc that are such that Sigma rho (vertical bar x vertical bar mu(x) < infinity for increasing regularly varying or slowly varying functions rho, for instance, s vertical bar -> (1 + s)(alpha), alpha is an element of(0, 2], or s vertical bar...
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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...
