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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...
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作者：Baxendale, Peter; Wong, Ting-Kam Leonard
作者单位：University of Southern California; University of Toronto
摘要：Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gradient maps define novel investment strategies. The gradient maps may also be regarded as optimal transport maps on the simplex. In this paper we construct and study probability ...
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作者：Racz, Miklos Z.; Sridhar, Anirudh
作者单位：Princeton University
摘要：We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly growing graphs, such as uniform attachment (UA) or preferential attachment (PA). Given such a model, a pair of graphs (G(1), G(2)) is grown in two stages: until time t(*) they are grown together (i.e., G(1) = G(2)), after which they grow independently according to...
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作者：Baldasso, Rangel; Pereira, Alan; Reis, Guilherme
作者单位：Bar Ilan University; Universidade Federal de Alagoas; Universidade Federal da Bahia
摘要：We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the path-dependent McKean-Vlasov diffusion associated t...
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作者：Coja-Oghlan, Amin; Mueller, Noela; Ravelomanan, Jean B.
作者单位：Dortmund University of Technology; Eindhoven University of Technology
摘要：Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as replica symmetry in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model...
