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作者：Del Moral, P.; Tugaut, J.
作者单位：Universite de Bordeaux
摘要：The ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov-type particle interpretation of the Kalman-Bucy diffusions. In contrast to more conventional particle filters and nonlinear Markov processes, these models are designed in terms of a diffusion process with a diffusion matrix that depends on particle...
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作者：Xu, Liping
作者单位：Sorbonne Universite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials [gamma epsilon ( -1, 0)] using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the class of all weak solutions, assuming only that the initial condition has a finite entropy and a finite moment of sufficiently high order. We also consider the Nanbu N-stochastic particle system, which approximates the weak solution. We use a probabilistic...
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作者：Krishnan, Arjun; Quastel, Jeremy
作者单位：University of Rochester; University of Toronto
摘要：The free-energy fluctuations of the discrete directed polymer in 1 + 1 dimensions is conjecturally in the Tracy-Widom universality class at all finite temperatures and in the intermediate disorder regime. Seppalainen's log-gamma polymer was proven to have GUE Tracy-Widom fluctuations in a restricted temperature range by Borodin, Corwin and Remenik [Comm. Math. Phys. 324 (2013) 215-232]. We remove this restriction, and extend this result into the intermediate disorder regime. This result also i...
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作者：Li, Yao
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：We consider a stochastic energy exchange model that models the 1-D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of the nonequilibrium steady state (NESS) and, furthermore, the polynomial speed of convergence to the NESS. Our result shows that the asymptotic properties of this model and its deterministic dynamical system origin are consistent. The proof uses a new technique called the induced chain method. We partition the state...
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作者：Bolley, Francois; Chafai, Djalil; Fontbona, Joaquin
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：We study the long-time behavior of the dynamics of interacting planar Brownian particles, confined by an external field and subject to a singular pair repulsion. The invariant law is an exchangeable Boltzmann-Gibbs measure. For a special inverse temperature, it matches the Coulomb gas known as the complex Ginibre ensemble. The difficulty comes from the interaction which is not convex, in contrast with the case of one-dimensional log-gases associated with the Dyson Brownian motion. Despite the ...
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作者：Davis, Erik; Sethuraman, Sunder
作者单位：University of Arizona
摘要：Given a graph, the popular modularity clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this paper, we discuss scaling limits of this method with respect to random geometric graphs constructed from i.i.d. points X-n = {X-1, X-2,..., X-n}, distributed according to a probability measure nu supported on a bounded domain D subset of R-d. Among other results, we show, via a Gamma convergence framework, a geometric form of consistency: Wh...
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作者：Fountoulakis, Nikolaos; Mueller, Tobias
作者单位：University of Birmingham; Utrecht University; University of Groningen
摘要：We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are associated with so-called complex networks. The model is controlled by two parameters alpha and nu where, roughly speaking, alpha controls the exponent of the power law and nu controls the average degree. Refining earlier results, we are able to show a law of large ...
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作者：Sasada, Makiko
作者单位：University of Tokyo
摘要：In the diffusive hydrodynamic limit for a symmetric interacting particle system (such as the exclusion process, the zero range process, the stochastic Ginzburg-Landau model, the energy exchange model), a possibly nonlinear diffusion equation is derived as the hydrodynamic equation. The bulk diffusion coefficient of the limiting equation is given by the Green-Kubo formula and it can be characterized by a variational formula. In the case the system satisfies the gradient condition, the variation...
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作者：Litvak, Alexander E.; Tikhomirov, Konstantin
作者单位：University of Alberta; University of Alberta; Princeton University
摘要：Let X be an n-dimensional random centered Gaussian vector with independent but not identically distributed coordinates and let T be an orthogonal transformation of R-n. We show that the random vector Y = T (X) satisfies E Sigma j=1(k) j-min (i)(<= n) X-i(2 )<= CE Sigma j=1(k) j-min(i)(<= n) Y-i(2 ) for all k <= n, where j-min denotes the jth smallest component of corresponding vector and C >0 is a universal constant. This resolves (up to a multiplicative constant) an old question of S. Mallat ...
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作者：Blanchard, Romain; Carassu, Laurence
作者单位：Universite de Reims Champagne-Ardenne
摘要：This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.
