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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：Abe, Yoshihiro; Biskup, Marek
作者单位：Chiba University; University of California System; University of California Los Angeles
摘要：We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by N) versions D-N subset of Z(2) of bounded open domains D subset of R-2. Upon exit from D-N, the walk lands on a boundary vertex and then reenters D-N through a random boundary edge in the next step. In the parametrization by the local time at the boundary vertex we prove that, at times corresponding to a theta-multiple of the cover time of D-N, the sets of suitably defined lambda-thick (i.e.,...
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作者：Bakhtin, Yuri; Chen, Hong-Bin
作者单位：New York University
摘要：We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1 + 1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the...
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作者：De Ponti, Nicolo; Mondino, Andrea
作者单位：International School for Advanced Studies (SISSA); University of Oxford
摘要：Inspired by the recent theory of Entropy-Transport problems and by the D-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly different total mass. We provide several explicit examples of such distances, where a prominent role is played by a geodesic metric based on the Hellinger-Kantorovich distance. Moreover, we discuss some limiting cases of the theory, recovering the pure transport D-dista...
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作者：Beiglboeck, M.; Jourdain, B.; Margheriti, W.; Pammer, G.
作者单位：University of Vienna; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Our main result is to establish stability of martingale couplings: suppose that pi is a martingale coupling with marginals mu, nu. Then, given approximating marginal measures (mu) over tilde approximate to mu, (nu) over tilde approximate to nu in convex order, we show that there exists an approximating martingale coupling (pi) over tilde approximate to pi with marginals (mu) over tilde, (nu) over tilde. In mathematical finance, prices of European call/put option yield information on the margin...
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作者：Dereudre, David
作者单位：Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the bond percolation model on the lattice Z(d) (d >= 2) with the constraint to be fully connected. Each edge is open with probability p is an element of (0, 1), closed with probability 1- p and then the process is conditioned to have a unique open connected component (bounded or unbounded). The model is defined on Z(d) by passing to the limit for a sequence of finite volume modelswith general boundary conditions. Several questions and problems are investigated: existence, uniquenes...
