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作者：Bou-Rabee, Ahmed; Morfe, Peter S.
作者单位：University of Chicago
摘要：Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dimensions has a scaling limit described by a first-order Hamilton-Jacobi equation and give an explicit formula for the limiting Hamiltonian, which is both non-coercive and non-convex. This contrasts with convex peeling, which converges to curvature flow. The proof involves direct geometric manipulations in the same spir...
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作者：Boedihardjo, March; Strohmer, Thomas; Vershynin, Roman
作者单位：Michigan State University; University of California System; University of California Davis; University of California System; University of California Irvine
摘要：Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex-but very common-machine learning tasks such as clustering or clas...
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作者：Goncalves, P.; Jara, M.; Marinho, R.; Menezes, O.
作者单位：Universidade de Lisboa; Universidade Federal de Santa Maria (UFSM); Universidade Federal da Bahia
摘要：We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d <= 3\documentclass[12pt]{minimal} \us...
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作者：Riera, Armand; Rosales-Ortiz, Alejandro
作者单位：Universite Paris Cite; Sorbonne Universite; University of Zurich
摘要：We construct an additive functional playing the role of the local time-at a fixed point x-for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees satisfy a special Markov property which can be thought as a spatial version of the classical Markov property. Then, we construct our additive functional by an approximation procedure and we characterize the support of its Lebesgue-Stieltjes measure. We also give an equivalent construction in terms o...
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作者：Clozeau, Nicolas; Mattesini, Francesco
作者单位：Institute of Science & Technology - Austria; University of Munster; Max Planck Society
摘要：We study a random matching problem on closed compact 2-dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m = m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures mu(n) and v(m) is quantitat...
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作者：Berestycki, Nathanael; van Engelenburg, Diederik
作者单位：University of Vienna
摘要：We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al. (Ann Probab 29...
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作者：Landon, Benjamin; Lopatto, Patrick; Sosoe, Philippe
作者单位：University of Toronto; Brown University; Cornell University
摘要：We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem fo...
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作者：Feng, Yu; Peltola, Eveliina; Wu, Hao
作者单位：Tsinghua University; Aalto University; University of Bonn
摘要：We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q is an element of [ 1 , 4 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsf...
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作者：Dolera, Emanuele; Favaro, Stefano; Mainini, Edoardo
作者单位：University of Pavia; University of Turin; University of Genoa
摘要：In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the ...
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli bond percolation on transitive nonamenable graphs under the L-2 boundedness condition (p(c) < p(2 -> 2)). Surprisingly, we find that the volume growth of infinite clusters is always purely exponential (that is, the subexponential corrections to growth are bounded) in the regime p(c) < p < p(2 -> 2), even when the ambient graph has unbounded corrections to exponential growth. For p slightly larger than...
