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作者：Chiarini, Alberto; Nitzschner, Maximilian
作者单位：University of California System; University of California Los Angeles; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate level-set percolation of the discrete Gaussian free field on Zd, d = 3, in the strongly percolative regime. We consider the event that the level-set of theGaussian free field below a level a disconnects the discrete blow-up of a compact set A. Rd from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of theGaussian free field deviate from a specific multiple of the harmonic potential of A, when disconne...
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作者：Prigent, Martin; Roberts, Matthew I.
作者单位：University of Bath
摘要：We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in one dimension, for which such exceptional times are known not to exist. In fact we show that the set of exceptional times has Hausdorff dimension 1/2 almost surely, and give bounds on the rate at which the walk diverges at such times. We also show noise sensi...
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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：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：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：Addario-Berry, L.; Cairns, H.; Devroye, L.; Kerriou, C.; Mitchell, R.
作者单位：McGill University; Cornell University; McGill University
摘要：We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (Pemantle's Min-Plus Binary Tree, 2017.[math.PR]), and to the critical random hierarchical lattice studied by Hambly and Jordan (Adv Appl Probab 36(3):824-838, 2004. 10.1239/aap/1093962236). We prove distributional convergence for the processes, after rescaling,...
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作者：Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; New York University; NYU Shanghai; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process fro...
