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作者：Pillai, Natesh S.; Smith, Aaron
作者单位：Harvard University; University of Ottawa
摘要：Determining the total variation mixing time of Kac's random walk on the special orthogonal group SO(n) has been a long-standing open problem. In this paper, we construct a novel non-Markovian coupling for bounding this mixing time. The analysis of our coupling entails controlling the smallest singular value of a certain random matrix with highly dependent entries. The dependence of the entries in our matrix makes it not amenable to existing techniques in random matrix theory. To circumvent thi...
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作者：Aldous, David
作者单位：University of California System; University of California Berkeley
摘要：Plant differently colored points in the plane; then let random points (Poisson rain) fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions converge (in some sense) to a random partition of the plane. We prove a weak version of this, showing that normalized empirical measures converge to Lebesgue measures on a random partition into measurable sets. Topological properties remain an open problem. In ...
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作者：Binotto, Giulia; Nourdin, Ivan; Nualart, David
作者单位：University of Barcelona; University of Luxembourg; University of Kansas
摘要：The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, of the nu-symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes the critical value H = (4l + 2)(-1), where l = l (.) = 1 is the largest natural number satisfying integral(1)(0) alpha(2j) nu(d alpha) = 1/2j+1 for all j = 0,..., l - 1. As a consequence, we derive a change-of-variable formula in distribution, where the correction term is a stochastic...
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作者：Timar, Adam
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：We prove that the infinite components of the Free Uniform Spanning Forest (FUSF) of a Cayley graph are indistinguishable by any invariant property, given that the forest is different from its wired counterpart. Similar result is obtained for the Free Minimal Spanning Forest (FMSF). We also show that with the above assumptions there can only be 0, 1 or infinitely many components, which solves the problem for the FUSF of Caylay graphs completely. These answer questions by Benjamini, Lyons, Peres...
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作者：Bordenave, Charles; Caputo, Pietro; Chafai, Djalil; Tikhomirov, Konstantin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Roma Tre University; Universite PSL; Universite Paris-Dauphine; Princeton University
摘要：Consider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral radius is close to the square root of the dimension. We conjecture that this holds true under the sole assumption of zero mean and unit variance. In other words, that there are no outliers in the circular law. In this work, we establish the conjecture in the ca...
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作者：Dobler, Christian; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We prove a fourth moment bound without remainder for the normal approximation of random variables belonging to the Wiener chaos of a general Poisson random measure. Such a result-that has been elusive for several years-shows that the so-called 'fourth moment phenomenon', first discovered by Nualart and Peccati [Ann. Probab. 33 (2005) 177-193] in the context of Gaussian fields, also systematically emerges in a Poisson framework. Our main findings are based on Stein's method, Malliavin calculus ...
