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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).
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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 ...
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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...
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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 ...
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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...
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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...
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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 ...
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作者：Abraham, Romain; Delmas, Jean-Francois; Nassif, Michel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We give an invariance principle for very general additive functionals of conditioned Bienayme-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Levy tree. This includes the case when the offspring distribution has finite variance (the Levy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending...
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作者：Bao, Zhigang; Wang, Dong
作者单位：Hong Kong University of Science & Technology; National University of Singapore
摘要：In this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source. We will focus on the critical regime of the Baik-Ben Arous-Peche (BBP) phase transition and establish the distribution of the eigenvectors associated with the leading eigenvalues. The distribution is given in terms of a determinantal point process with extended Airy kernel. Our result can be regarded as an eigenvector counterpart of the BBP eigenvalue phase transitio...
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作者：Parraud, Felix
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Kyoto University
摘要：Let U-N = (U-1(N), ..., U-p(N)) be a p-tuple of N x N independent Haar unitary matrices and Z(NM) be any family of deterministic matrices in M-N(C) circle times M-M(C). Let P be a self-adjoint non-commutative polynomial. In Voiculescu (Int Math Res Notices 1:41-63, 1998), Voiculescu showed that the empirical measure of the eigenvalues of this polynomial evaluated in Haar unitary matrices and deterministic matrices converges towards a deterministic measure defined thanks to free probability the...
