-
作者：Athreya, Jayadev S.; Mj, Mahan; Roy, Parthanil
作者单位：University of Washington; University of Washington Seattle; Tata Institute of Fundamental Research (TIFR); Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We study extreme values of group-indexed stable random fields for discrete groups G acting geometrically on spaces X in the following cases: (1) G acts properly discontinuously by isometries on a CAT(-1) space X, (2) G is a lattice in a higher rank Lie group, acting on a symmetric space X, and (3) G is the mapping class group of a surface acting on its Teichmuller space. The connection between extreme values and the geometric action is mediated by the action of the group G on its limit set equ...
-
作者：Ahn, Andrew
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We study Markov chains formed by squared singular values of products of truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson index beta = 1, 2, 4 respectively) where time corresponds to the number of terms in the product. More generally, we consider the beta-Jacobi product process obtained by extrapolating to arbitrary beta > 0. For fixed time (i.e. number of factors is constant), we show that the global fluctuations are jointly Gaussian with explicit covariances. For...
-
作者：Bobrowski, Omer
作者单位：Technion Israel Institute of Technology; University of London; Queen Mary University London
摘要：We study the homology of random Cech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity'-the stage where the random complex is dense enough, so that its homology stabilizes and becomes isomorphic to that of the underlying topological space. Our results form a comprehensive high-dimensional analogue of well-known phenomena related to connectivity in the Erdos-Renyi graph and random geometric graphs. We first prove that there is a sequence of sharp phase ...
-
作者：Aidekon, Elie; Da Silva, William
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Sorbonne Universite; Universite Paris Cite
摘要：The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane H, obtained by cutting the excursion at horizontal levels. We prove that the associated growth-fragmentation is related to one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski in (Bertoin et al. Probab Theory Relat Field 172:663-724, 2018).
-
作者：Holroyd, Alexander E.; Janson, Svante; Wastlund, Johan
作者单位：University of Bristol; Uppsala University; Chalmers University of Technology
摘要：Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider ...
-
作者：Marcus, Adam W.; Spielman, Daniel A.; Srivastava, Nikhil
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Yale University; University of California System; University of California Berkeley
摘要：We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh and Szego in different contexts, and have been studied for a century. The asymmetric additive convolution, and the connection of all of them with random matrices, is new. By develo...
-
作者：Au, Benson
作者单位：University of California System; University of California Berkeley
摘要：Let (sigma((i))(N))(i is an element of I) be a family of symmetric permutations of the entries of a Wigner matrix W-N. We characterize the limiting traffic distribution of the corresponding family a o) of dependent Wigner matrices (W-N(N)sigma(i))(i is an element of I) in terms of the geometry of the permutations. We also consider the analogous problem for the limiting joint distribution of (W-N(N)sigma(i))(i is an element of I). In particular, we obtain a description in terms of semicircular ...
-
作者：De, Anindya; Nadimpalli, Shivam; Servedio, Rocco A.
作者单位：University of Pennsylvania; Columbia University
摘要：Many correlation inequalities for high-dimensional functions in the literature, such as the Harris-Kleitman inequality, the Fortuin-Kasteleyn-Ginibre inequality and the celebrated Gaussian Correlation Inequality of Royen, are qualitative statements which establish that any two functions of a certain type have non-negative correlation. Previous work has used Markov semigroup arguments to obtain quantitative extensions of some of these correlation inequalities. In this work, we augment this appr...
-
作者：Nutz, Marcel; Wiesel, Johannes
作者单位：Columbia University; Columbia University
摘要：We study the potential functions that determine the optimal density for epsilon-entropically regularized optimal transport, the so-called Schrodinger potentials, and their convergence to the counterparts in classical optimal transport, the Kantorovich potentials. In the limit epsilon -> 0 of vanishing regularization, strong compactness holds in L-1 and cluster points are Kantorovich potentials. In particular, the Schrodinger potentials converge in L-1 to the Kantorovich potentials as soon as t...
-
作者：Divol, Vincent
作者单位：New York University; New York University
摘要：Assume that we observe i.i.d. points lying close to some unknown d-dimensional C-k submanifold M in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the sample. After remarking that this problem is degenerate for a large class of standard losses (L-p, Hellinger, total variation, etc.), we focus on the Wasserstein loss, for which we build an estimator, based on kernel density estimation, whose rate of convergence depends on d and ...
