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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...
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作者：Guerra, Enrique; Valle, Glauco; Vares, Maria Eulalia
作者单位：Hebrew University of Jerusalem; Universidade Federal do Rio de Janeiro
摘要：We study ballisticity conditions for d-dimensional random walks in strong mixing environments, with underlying dimension d >= 2. Specifically, we introduce an effective polynomial condition similar to that given by Berger et al. (Comm. Pure Appl. Math. 77:1947-1973, 2014). In a mixing setup we prove that this condition implies the corresponding stretched exponential decay, and obtain an annealed functional central limit theorem for the random walk process centered at the limiting velocity. Thi...
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作者：Lammers, Piet
作者单位：Universite Paris Saclay
摘要：The interest is in models of integer-valued height functions on shift-invariant planar graphs whose maximum degree is three. We prove delocalisation for models induced by convex nearest-neighbour potentials, under the condition that each potential function is an excited potential, that is, a convex symmetric potential function V with the property that V(+/- 1) <= V(0) + log 2. Examples of such models include the discrete Gaussian and solid-on-solid models at inverse temperature beta <= log 2, ...
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作者：Gonzalez, Isaac; Horton, Emma; Kyprianou, Andreas E.
作者单位：University of Bath; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：Suppose that X = (X-t, t >= 0) is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities P-delta x, when issued from a unit mass at x is an element of E. For a general setting in which the first moment semigroup of X displays a Perron-Frobenius type behaviour, we show that, for k >= 2 and any positive bounded measurable function f on E, lim(t ->infinity) gk(t)E-delta x[< f, X-t >(k)] = C-k(x, f), where the constant C-k(x, ...
