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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 ...
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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...
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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...
