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作者：Feray, Valentin; Louf, Baptiste; Thevenin, Paul
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine
摘要：We study the asymptotic behaviour of random factorizations of the n-cycle into transpositions of fixed genus g > 0. They have a geometric interpretation as branched covers of the sphere and their enumeration as Hurwitz numbers was extensively studied in algebraic combinatorics and enumerative geometry. On the probabilistic side, several models and properties of permutation factorizations were studied in previous works, in particular minimal factorizations of cycles into transpositions (which c...
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作者：Ganguly, Shirshendu; Nam, Kyeongsik
作者单位：University of California System; University of California Berkeley; Korea Advanced Institute of Science & Technology (KAIST)
摘要：Large deviation behavior of the largest eigenvalue lambda(1) of Wigner matrices including those arising from an Erdos-Renyi random graph G(n, p) with i.i.d. random conductances on the edges has been the topic of considerable interest. However, despite several recent advances, not much is known when the underlying graph is sparse i.e., p -> 0, except the recent works (Bhattacharya et al., Ann Probab 49(4):1847-1885, 202 land Bhattacharya and Ganguly, SIAM J Discret Math, 2020) which consider th...
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作者：Bloznelis, Mindaugas; Goetze, Friedrich
作者单位：Vilnius University; University of Bielefeld
摘要：We study the distribution of a general class of asymptotically linear statistics which are symmetric functions of N independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a remainder of order o(N-1). The Edgeworth expansion is based on Hoeffding's decomposition which provides a stochastic expansion into a linear part, a quadratic part as well as smaller higher order parts. The validity of this Edgeworth expansion is proved under...
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作者：Lim, Tongseok; McCann, Robert J.
作者单位：Purdue University System; Purdue University; University of Toronto
摘要：Among probability measures on d-dimensional real projective space, one which maximizes the expected angle arccos (x/vertical bar x vertical bar . y/vertical bar y vertical bar) between independently drawn projective points x and y was conjectured to equidistribute its mass over the standard Euclidean basis {e(0), e(1), . . . , e(d)) by Fejes Toth (Acta Math Acad Sci Hung 10:13-19, 1959. https://doi.org/10.1007/BF02063286) . If true, this conjecture evidently implies the same measure maximizes ...
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作者：Nestoridi, Evita; Olesker-Taylor, Sam
作者单位：Princeton University; University of Cambridge
摘要：In a recent breakthrough, Teyssier (Ann Probab 48(5):2323-2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to s...
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作者：Liu, Jingbo
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We give a complete solution to an open problem of Thomas Cover in 1987 about the capacity of a relay channel in the general discrete memoryless setting without any additional assumptions. The key step in our approach is to lower bound a certain soft-max of a stochastic process by convex geometry methods, which is based on two ideas: First, the soft-max is lower bounded in terms of the supremum of another process, by approximating a convex set with a polytope with bounded number of vertices. Se...
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作者：Eldan, Ronen; Koehler, Frederic; Zeitouni, Ofer
作者单位：Weizmann Institute of Science; Massachusetts Institute of Technology (MIT)
摘要：We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincare inequality with respect to the natural Dirichlet form corresponding to Glauber dynamics, as soon as the operator norm of the interaction matrix is smaller than 1. The inequality implies a control on the mixing time of the Glauber dynamics. Our techniques rely on a localization procedure which establishes a structural result, stating that Ising measures may be decomposed into a mixture of measures...
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作者：Galashin, Pavel
作者单位：University of California System; University of California Los Angeles
摘要：Given a finite rhombus tiling of a polygonal region in the plane, the associated critical Z-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between boundary vertices in terms of the shape of the region. When the region is a regular polygon, our formula becomes an explicit trigonometric sum.
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作者：Della Maestra, Laetitia; Hoffmann, Marc
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a system of N interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time horizon, we investigate nonparametric estimation of the solution of the associated nonlinear Fokker-Planck equation, together with the drift term that controls the interactions, in a large population limit N -> infinity. We build data-driven kernel estimators a...
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作者：Samson, Paul-Marie
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. Leonard by replacing W-2-Wasserstein geodesics by Schrodinger bridges in the definition of entropic curvature (Leonard in Discrete Contin Dyn Syst A 34(4):1533-1574, 2014; Ann Probab 44(3):1864-1915, 2016; in: Gigli N (ed) Measure theory in non-smooth spaces. Sciendo Migration,Warsaw, pp 194-242, 2017). As a remarkable fact, as a temperature parameter goes to zero, these Schrodinger bridg...
