-
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....
-
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.
-
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...
-
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...
-
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-...
-
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 (...
-
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 .
-
作者：Bourgade, Paul; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：In the first part of this article (Bourgade et al. arXiv:1206.1449, 2012), we proved a local version of the circular law up to the finest scale for non-Hermitian random matrices at any point with for any independent of the size of the matrix. Under the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we extend this result to include the edge case . Without the vanishing third moment assumption, we pro...
-
作者：Goldenshluger, A.; Lepski, O.
作者单位：University of Haifa; Aix-Marseille Universite
摘要：We address the problem of adaptive minimax density estimation on with -loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in order over the complete scale o...
-
作者：Petrov, Leonid
作者单位：Northeastern University; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m = 1, ... , N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed Nth row. We obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble (and also of its q-deformation). This provides new tools for asymptotic analysis of uniformly random lozenge tilings of polygons on the trian...
