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作者：Bordenave, Charles; Lugosi, Gabor; Zhivotovskiy, Nikita
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Pompeu Fabra University; ICREA; Alphabet Inc.; Google Incorporated
摘要：We investigate the noise sensitivity of the top eigenvector of a Wigner matrix in the following sense. Let v be the top eigenvector of an NxN Wigner matrix. Suppose that k randomly chosen entries of the matrix are resampled, resulting in another realization of the Wigner matrix with top eigenvector v[k]. We prove that, with high probability, when kMUCH LESS-THANN5/3-o(1), then v and v[k] are almost collinear and when k >> N5/3, then v[k] is almost orthogonal to v.
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作者：Gnedin, Alexander; Iksanov, Alexander
作者单位：University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity. In the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in Ewens' and mor...
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作者：Bonis, Thomas
作者单位：Universite Paris Saclay
摘要：We use Stein's method to bound the Wasserstein distance of order 2 between a measure nu and the Gaussian measure using a stochastic process (X-t)(t >= 0) such that X-t is drawn from nu for any t > 0. If the stochastic process (X-t)(t >= 0) satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds onWasserstein distances of any order p >= 1. Using our results, we provide convergence rates for the multi-dimensional central limit theorem in terms of Wasserst...
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作者：Berestycki, Nathanael; Powell, Ellen; Ray, Gourab
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Victoria
摘要：We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.
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作者：Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian
作者单位：University of Edinburgh; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Exeter; University of Warwick
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作者：Han, Yanjun; Jiao, Jiantao; Mukherjee, Rajarshi
作者单位：Stanford University; University of California System; University of California Berkeley; Harvard University; Harvard T.H. Chan School of Public Health
摘要：We provide a complete picture of asymptotically minimax estimation of L-r-norms (for any r >= 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski et al. (Probab Theory Relat Fields 113(2):221-253, 1999), who considered the cases of r = 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bounds) over Holder spaces. We additionally consider the case of asymptotica...
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作者：Lyons, Russell; White, Graham
作者单位：Indiana University System; Indiana University Bloomington
摘要：Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graph...
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作者：Peres, Yuval; Tanaka, Ryokichi; Zhai, Alex
作者单位：Tohoku University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Stanford University
摘要：We analyze a Markov chain, known as the product replacement chain, on the set of generating n-tuples of a fixed finite group G. We show that as n. 8, the totalvariation mixing time of the chain has a cutoff at time 3 2 n log n with window of order n. This generalizes a result of Ben-Hamou and Peres (who established the result for G = Z/2) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is O(n ...
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作者：Aru, Juhan; Lupu, Titus; Sepulveda, Avelio
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We introduce the first passage set (FPS) of constant level -a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the boundary by a path on which the GFF does not go below -a. It is, thus, the two-dimensional analogue of the first hitting time of -a by a one-dimensional Brownian motion. We provide an axiomatic characterization of the FPS, a continuum construction using level lines, ...
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作者：Gordina, Maria; Roeckner, Michael; Teplyaev, Alexander
作者单位：University of Connecticut; University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We consider a perturbation of a Hilbert space-valued Ornstein-Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls in the Hilbert space uniformly in time. First we introduce a new notion of generalized solutions for such equations which we call pseudo-weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation. Then ...
