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作者：Barchiesi, Marco; Julin, Vesa
作者单位：University of Naples Federico II; University of Jyvaskyla
摘要：We study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. The second term is in competition with the perimeter, balancing the mass with respect to the origin, and because of that the solution is not always the half-space. We characterize all the minimizers of this functional, when the volume is close to one, by proving that the minimizer is either the half-space or the symmetric strip, depending on the strength ...
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作者：Lytova, Anna; Tikhomirov, Konstantin
作者单位：University of Opole; University System of Georgia; Georgia Institute of Technology
摘要：We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let A be an nxn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\times n$$\end{document}|I|=m||vI||>= m3/2n3/2logCn||v||\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
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作者：Eldan, Ronen
作者单位：Weizmann Institute of Science
摘要：The analysis of various models in statistical physics relies on the existence of decompositions of measures into mixtures of product-like components, where the goal is to attain a decomposition into measures whose entropy is close to that of the original measure, yet with small correlations between coordinates. We prove a related general result: For every measure mu on Rn and every epsilon>0, there exists a decomposition mu=integral mu theta dm(theta) such that H(mu)-E theta similar to mH(mu t...
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作者：Miller, Jason; Qian, Wei
作者单位：University of Cambridge
摘要：We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLE kappa. These hypotheses are satisfied by the LQG metric for gamma = root 8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each gamma is an element of (0, 2...
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作者：Grama, Ion; Lauvergnat, Ronan; Le Page, Emile
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let (Xn) n0 be a Markov chain with values in a finite state space X starting at X0 = x. X and let f be a real function defined on X. Set Sn = nk =1 f ( Xk), n 1. For any y. R denote by ty the first time when y + Sn becomes non-positive. We study the asymptotic behaviour of the probability Px y + Sn. [z, z + a], ty > n as n.+8. We first establish for this probability a conditional version of the local limit theorem of Stone. Then we find for it an asymptotic equivalent of order n3/2 and give a ...
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作者：Gwynne, Ewain; Holden, Nina; Miller, Jason
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLE kappa curve for kappa not equal 4. Our proof is based on the relationship between SLE and Liouville quantum gravity together with the one-dimensional KPZ formula of Rhodes and Vargas (ESAIM Probab Stat 15:358-371, 2011) and the KPZ formula of Gwynne et al. (Ann Probab, 2...
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作者：Caputo, Pietro; Quattropani, Matteo
作者单位：Roma Tre University
摘要：We consider sparse digraphs generated by the configuration model with given in-degree and out-degree sequences. We establish that with high probability the cover time is linear up to a poly-logarithmic correction. For a large class of degree sequences we determine the exponent gamma >= 1 of the logarithm and show that the cover time grows as n log(gamma) (n), where n is the number of vertices. The results are obtained by analysing the extremal values of the stationary distribution of the digra...
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作者：Borga, Jacopo
作者单位：University of Zurich
摘要：We set up a new notion of local convergence for permutations and we prove a characterization in terms of proportions of consecutive pattern occurrences. We also characterize random limiting objects for this new topology introducing a notion of shift-invariant property (corresponding to the notion of unimodularity for random graphs). We then study two models in the framework of random pattern-avoiding permutations. We compute the local limits of uniform rho-avoiding permutations, for vertical b...
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作者：Nourdin, Ivan; Nualart, David
作者单位：University of Luxembourg; University of Kansas
摘要：Let X = {X-n}(n is an element of Z) be zero-mean stationary Gaussian sequence of random variables with covariance function rho satisfying rho(0) = 1. Let phi : R -> R be a function such that E[phi(X-0)(2)] < infinity and assume that phi has Hermite rank d >= 1. The celebrated Breuer-Major theorem asserts that, if Sigma(r is an element of Z) vertical bar rho(r)vertical bar(d) < infinity then the finite dimensional distributions of 1/root n Sigma(left perpendicularn.right perpenducular-1)(i=0) p...
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作者：Gwynne, Ewain; Holden, Nina; Sun, Xin
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We introduce a general technique for proving estimates for certain random planar maps which belong to the gamma-Liouville quantum gravity (LQG) universality class for gamma is an element of(0,2) The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d. increments via a mating-of-trees bijection, and includes the uniform infinite planar triangulation (UIPT;gamma=8/3and planar maps weighted by the number of different spanning trees (...
