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作者：Mourrat, Jean-Christophe
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimensi...
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作者：Paouris, Grigoris; Pivovarov, Peter; Zinn, Joel
作者单位：Texas A&M University System; Texas A&M University College Station; University of Missouri System; University of Missouri Columbia
摘要：We prove a central limit theorem for the volume of projections of the cube onto a random subspace of dimension , when is fixed and . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.
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作者：Castillo, Ismael; Kerkyacharian, Gerard; Picard, Dominique
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.
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作者：Drewitz, Alexander; Sousi, Perla; Sun, Rongfeng
作者单位：Columbia University; University of Cambridge; National University of Singapore
摘要：We prove a new rearrangement inequality for multiple integrals, which partly generalizes a result of Friedberg and Luttinger (Arch Ration Mech 61:35-44, 1976) and can be interpreted as involving symmetric rearrangements of domains around . As applications, we prove two comparison results for general L,vy processes and their symmetric rearrangements. The first application concerns the survival probability of a point particle in a Poisson field of moving traps following independent L,vy motions....
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作者：Friz, Peter; Oberhauser, Harald
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its L,vy area) as rough path noise the solution coincides with the standard variational solution of the SPDE.
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作者：Abramson, Joshua; Evans, Steven N.
作者单位：University of California System; University of California Berkeley
摘要：For , the -Lipschitz minorant of a function is the greatest function such that and for all , should such a function exist. If is a real-valued L,vy process that is not pure linear drift with slope , then the sample paths of have an -Lipschitz minorant almost surely if and only if . Denoting the minorant by , we investigate properties of the random closed set , which, since it is regenerative and stationary, has the distribution of the closed range of some subordinator made stationary in a suit...
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作者：Debussche, Arnaud; Romito, Marco
作者单位：University of Pisa
摘要：We prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic Navier-Stokes equations in dimension . In particular, under very mild assumptions on the noise, we prove that finite dimensional projections of the solutions have densities with respect to the Lebesgue measure which have some smoothness when measured in a Besov space. This is proved thanks to a new argument inspired by an idea introduced in (Fournier and Printe...
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作者：Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie; Tetali, Prasad
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Paris Nanterre; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Pr,kopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings. To illustrate through examples, we apply our results to the complete graph and to the hypercube for which our results are optimal-...
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作者：Basu, Riddhipratim; Sly, Allan
作者单位：University of California System; University of California Berkeley
摘要：We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. Grimmett et al. (Random Str Algorithm 37(1):85-99, 2010) asked whether there exists an increasing -Lipschitz embedding from one i.i.d. Bernoulli sequence into an independent copy with positive probability. We give a positive answer for large enough . A closely related problem is to show that two independent Poisson processes on are roughly isometric (...
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作者：Viklund, Fredrik Johansson; Rohde, Steffen; Wong, Carto
作者单位：Columbia University; University of Washington; University of Washington Seattle
摘要：We prove that for almost every Brownian motion sample, the corresponding SLE curves parameterized by capacity exist and change continuously in the supremum norm when varies in the interval , where . We estimate the -dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with .
