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作者：Dedecker, Jerome; Merlevede, Florence; Peligrad, Magda
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; University System of Ohio; University of Cincinnati
摘要：In this paper, we consider partial sums of martingale differences weighted by random variables drawn uniformly on the sphere, and globally independent of the martingale differences. Combining Lindeberg's method and a series of arguments due to Bobkov, Chistyakov and G & ouml;tze, we show that the Kolmogorov distance between the distribution of these weighted sums and the limiting Gaussian is super-fast of order (log n)2/n, under conditions allowing us to control the higher-order conditional mo...
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作者：Jackson, Joe; Lacker, Daniel
作者单位：University of Chicago; Columbia University
摘要：We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents, and the distributed problem, in which each agent observes only its own state. Our main results are sharp nonasymptotic bounds on the gap between these two problems, measured both in terms of their value functions and optimal states. Along the way, we develop ...
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作者：Champagnat, Nicolas; Hass, Vincent
作者单位：Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Universite Marie et Louis Pasteur
摘要：In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling rate modeling competition pressure driving selection and a mutation rate where mutations occur during life. In this model, the population state at fixed time is given as a measure on the space of phenotypes and the evolution of the population is described by ...
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作者：Aldous, David; Pittel, Boris
作者单位：University of California System; University of California Berkeley; University System of Ohio; Ohio State University
摘要：In the critical beta-splitting model of a random n-leaf binary tree, leaf- sets are recursively split into subsets, and a set of m leaves is split into subsets containing i and m - i leaves with probabilities proportional to 1/i(m - i). We study the continuous-time model in which the holding time before that split is exponential with rate hm-1, the harmonic number. We (sharply) evaluate the first two moments of the time-height Dn and of the edge-height Ln of a uniform random leaf (i.e., the le...
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作者：Bou-rabee, Nawaf; Marsden, MILO.
作者单位：Rutgers University System; Rutgers University Camden; Rutgers University New Brunswick; Stanford University
摘要：A randomized time integrator is suggested for unadjusted Hamiltonian Monte Carlo (uHMC) which involves a very minor modification to the usual Verlet time integrator, and hence, is easy to implement. For target distributions of the form mu(dx) proportional to e-U(x) dx where U : Rd -> R >= 0 is K-strongly convex but only L-gradient Lipschitz, and initial distributions epsilon with finite second moment, coupling proofs reveal that an epsilon-accurate approximation of the target distribution in L...
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作者：Shen, Xiao
作者单位：Utah System of Higher Education; University of Utah
摘要：The study of Kadar-Parsi-Zhang (KPZ) universality class has been a subject of great interest among mathematicians and physicists over the past three decades. A notably successful approach for analyzing KPZ models is the coupling method, which hinges on understanding random growth from stationary initial conditions defined by Busemann functions. To advance in this direction, we investigate the independence property of the Busemann function across multiple directions in various exactly solvable ...
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作者：Banas, L'Umbomir; Gess, Benjamin; Neuss, Marius
作者单位：University of Bielefeld; Max Planck Society; Deutsche Bundesbank
摘要：We study scaling limits of the weakly driven Zhang and the Bak- Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation (PDE) with singular-degenerate diffusion. In addition, the deterministic BTW model is shown to converge to a singular-degenerate PDE. Alternatively, the proof of the scaling limit can be understood as a convergence proof of a finite-difference discretization for singular-deg...
