Probability Theory and Related Fields

最新文章

• Partial estimation of covariance matrices AI翻译
  作者：Levina, Elizaveta; Vershynin, Roman
  作者单位：University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
  摘要：A classical approach to accurately estimating the covariance matrix I pound of a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller sample sizes, thus calling for estimation guarantees in the regime . We show that a sample of size n = O(m log(6) p) is sufficient to accurately estimate in operator norm an arbitrary symmetric part of I pound consisting of m a parts per thousand currency ...
• Properties of isoperimetric, functional and Transport-Entropy inequalities via concentration AI翻译
  作者：Milman, Emanuel
  作者单位：University of Toronto
  摘要：Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of these inequalities with respect to perturbation of the measure is obtained. The extent of the perturbation is measured using several different distances between perturbed and original measure, such as a one-sided L (a) bound on the ratio between their densities...
• Singular perturbations to semilinear stochastic heat equations AI翻译
  作者：Hairer, Martin
  作者单位：University of Warwick
  摘要：We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter epsilon tends to zero, their solutions converge to the 'wrong' limit, i.e. they do not converge to the solution obtained by simply setting epsilon = 0. A similar effect is also observed for some (formally) small stochastic perturbations of a deterministic semilinear parabolic PDE. Our proofs are based on a...
• Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case AI翻译
  作者：Barbu, Viorel; Roeckner, Michael; Russo, Francesco
  作者单位：Alexandru Ioan Cuza University; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; ENSTA Paris
  摘要：We consider a possibly degenerate porous media type equation over all of R-d with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analyti...
• Integration by parts formula and applications to equations with jumps AI翻译
  作者：Bally, Vlad; Clement, Emmanuelle
  作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147-235, 1983) fails.
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations AI翻译
  作者：Hairer, M.; Mattingly, J. C.; Scheutzow, M.
  作者单位：University of Warwick; New York University; Duke University; Technical University of Berlin
  摘要：There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of Harris' theorem. The first uses the existence of couplings which draw the solutions together as time goes to infinity. Such asymptotic couplings were central to (Mattingly and Sinai...
• Quasi-stationary distributions for structured birth and death processes with mutations AI翻译
  作者：Collet, Pierre; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile; Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that th...
• Spatial random permutations with small cycle weights AI翻译
  作者：Betz, Volker; Ueltschi, Daniel
  作者单位：University of Warwick
  摘要：We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.
• The covariant measure of SLE on the boundary AI翻译
  作者：Alberts, Tom; Sheffield, Scott
  作者单位：University of Toronto; Massachusetts Institute of Technology (MIT)
  摘要：We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with R, in the range 4 < kappa < 8. The measure is a function of the SLE path in question. Assuming that boundary measures transform in a d-dimensional way (where d is the Hausdorff dimension of gamma boolean AND R), we show that the measure we construct is (up to multiplicative constant) the unique measure-valued function of the SLE path that satisfies the Domain Markov property.
• Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time AI翻译
  作者：Heydenreich, Markus; van der Hofstad, Remco
  作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
  摘要：For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (Comm Math Phys 270(2):335-358, 2007). This improvement finally settles a conjecture by Aizenman (Nuclear Phys B 485(3):551-582, 1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical p...