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作者：Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Roma Tre University
摘要：Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph G = (V, E) dual to the biased voter model on G. Our main goal is tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as vertical bar V vertical bar -> infinity. Our results allow...
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作者：Pain, Michel; Senizergues, Delphin
作者单位：New York University; University of British Columbia
摘要：Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of weights, the first order for the height of such trees has been recently established by one of the authors. In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions. Our met...
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作者：Bao, Zhigang; He, Yukun
作者单位：Hong Kong University of Science & Technology; City University of Hong Kong
摘要：Let FN and F be the empirical and limiting spectral distributions of an N x N Wigner matrix. The Cramer-von Mises (CvM) statistic is a classical goodness-of-fit statistic that characterizes the distance between FN and F in L2-norm. In this paper, we consider a mesoscopic approximation of the CvM statistic for Wigner matrices, and derive its limiting distribution. In the Appendix, we also give the limiting distribution of the CvM statistic (without approximation) for the toy model CUE.
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作者：Hill, Max; Legried, Brandon; Roch, Sebastien
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Michigan System; University of Michigan
摘要：We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as mod-eled by a coalescent process) and gene duplication and loss (as modeled by a branching process). Through a probabilistic analysis of the model, we derive sample complexity bounds for widely used quartet-based inference methods that highlight the effect of the duplication and loss rates in both subcritical and supercritical regimes.
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作者：Ehrlacher, Virginie; Lelievre, Tony; Monmarche, Pierre
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Paris Cite; Sorbonne Universite
摘要：We analyze and propose variants of the adaptive biasing force method. First, we prove the convergence of a version of the algorithm where the biasing force is estimated using a weighted occupation measure, with an explicit asymptotic variance. Second, we propose a new flavour of the algorithm adapted to high-dimensional reaction coordinates, for which the standard approaches suffer from the curse of dimensionality. More precisely, the free energy is approximated by a sum of tensor products of ...
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作者：Noack, Christian; Sosoe, Philippe
作者单位：Cornell University
摘要：Seppalainen and Valko showed in (ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010) 451-476) that for a suitable choice of parameters, the variance growth of the free energy of the stationary O'Connell-Yor polymer is governed by the exponent 2/3, characteristic of models in the KPZ universality class. We develop exact formulas based on Gaussian integration by parts to relate the cumulants of the free energy, log Z(n,t)(theta), to expectations of products of quenched cumulants of the time of the fir...
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作者：Bartl, Daniel; Mendelson, Shahar
作者单位：University of Vienna; Australian National University
摘要：We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form min(x is an element of chi) E[F (x, xi)] when the given data is a finite independent sample selected according to xi. The procedure is based on a median-of-means tournament, and is the first procedure that exhibits the optimal statistical performance in heavy tailed situations: we recover the asymptotic rates dictated by the central limit theorem in a nonasymptotic manner on...
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作者：Flandoli, Franco; Hofmanova, Martina; Luo, Dejun; Nilssen, Torstein
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Agder
摘要：We are concerned with the problem of global well-posedness of the 3D Navier-Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our mai...
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作者：Holden, Nina; Lyons, Russell
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Indiana University System; Indiana University Bloomington
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作者：Guillin, Arnaud; Liu, Wei; Wu, Liming; Zhang, Chaoen
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
摘要：In this paper we consider a mean field particle systems whose confinement potentials have many local minima. We establish some explicit and sharp estimates of the spectral gap and logarithmic Sobolev constants uniform in the number of particles. The uniform Poincare inequality is based on the work of Ledoux (In Seminaire de Probabilites, XXXV (2001) 167194, Springer) and the uniform logarithmic Sobolev inequality is based on Zegarlinski's theorem for Gibbs measures, both combined with an expli...
