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作者：Nutz, Marcel; Wiesel, Johannes
作者单位：Columbia University; Columbia University
摘要：We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr delta dinger potentials, describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian or, ...
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作者：Comets, Francis; Dalmau, Joseba; Saglietti, Santiago
作者单位：Universite Paris Cite; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of Z and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. and heavy tailed, and where each block sticks to the interface at the first point of contact with probability p (otherwise, it falls straight down until it lands on a bloc...
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作者：Angel, Omer; Holmes, Mark; Ramirez, Alejandro
作者单位：University of British Columbia; University of Melbourne; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：We give nontrivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions and verify a conjecture of Benjamini, Kozma and Schapira. To the best of our knowledge, these are the first nontrivial results for this two-dimensional model.
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作者：Janson, Svante; Louf, Baptiste
作者单位：Uppsala University
摘要：We study uniformly random maps with a single face, genus g, and size n, as n, g -infinity with g = o(n), in continuation of several previous works on the geometric properties of high genus maps. We calculate the number of short simple cycles, and we show convergence of their lengths (after a well-chosen rescaling of the graph distance) to a Poisson process, which happens to be exactly the same as the limit law obtained by Mirzakhani and Petri (Comment. Math. Helv. 94 (2019) 869-889) when they ...
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作者：Jaramillo, Arturo; Nourdin, Ivan; Nualart, David; Peccati, Giovanni
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Luxembourg; University of Kansas
摘要：We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form [GRAPHICS] . where B={B-t; t >= 0} is a fBm with Hurst parameter H is an element of(0,1), f is a suitable test function and lambda is an element of R. We develop our study by distinguishing two regimes which exhibit different behaviors. When H is an element of(0,1/3), we show that a suitable renormalization of (0.1), compensated by a multiple of the local time of B, conv...
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作者：Lyons, Russell; White, Graham
作者单位：Indiana University System; Indiana University Bloomington
摘要：Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cay-ley graphs that arise from Coxeter systems but not for all Cayley graphs. On finite Cayley graphs, we show that the distance-in various senses-to stationarity is monotone decreasing in the rates for Coxeter systems and for abelian groups but not for all Cayley graphs. We also...
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作者：Alt, Johannes; Ducatez, Raphael; Knowles, Antti
作者单位：University of Geneva; New York University; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the adjacency matrix A of the Erdos-Renyi graph on N ver-tices with edge probability d/N. For (log log N)4 << d < log N, we prove that the eigenvalues near the spectral edge form asymptotically a Poisson point process and the associated eigenvectors are exponentially localized. As a corollary, at the critical scale d kappa log N, the limiting distribution of the largest nontrivial eigenvalue does not match with any previously known dis-tribution. Together with (Comm. Math. Phys. 38...
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作者：Halberstam, Noah; Hutchcroft, Tom
作者单位：University of Cambridge; California Institute of Technology
摘要：We prove that if (X-n)(n >= 0) is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then (X-n)(n >= 0) has infinitely many cut times almost surely. This condition applies in particular to any graph of spectral dimension strictly larger than 2. In fact, our proof applies to general (possibly nonreversible) Markov chains satisfying a similar decay condition for the Green's function that is sharp for birth-death chains. We deduce...
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作者：Najnudel, Joseph; Paquette, Elliot; Simm, Nick
作者单位：University of Bristol; McGill University; University of Sussex
摘要：We study the secular coefficients of N x N random unitary matrices UN drawn from the Circular-Ensemble which are defined as the coefficients of {zn} in the characteristic polynomial det(1 - zU*N). When > 4, we obtain a new class of limiting distributions that arise when both n and N tend to infinity simultaneously. We solve an open problem of Diaconis and Gamburd (Electron. J. Combin. 11 (2004/06) 2) by showing that, for = 2, the mid-dle coefficient of degree n = N2 j tends to zero as N -oo. W...
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作者：Das, Sayan; Ghosal, Promit
作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
摘要：We consider the Cole-Hopf solution of the (1 + 1)-dimensional KPZ equation started from the narrow wedge initial condition. In this article we ask how the peaks and valleys of the KPZ height function (centered by time/24) at any spatial point grow as time increases. Our first main result is about the law of iterated logarithms for the KPZ equation. As time variable t goes to infinity, we show that the limsup of the KPZ height function with the scaling by root t1/3(loglogt)2/3 is almost surely ...
