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作者：Kasprzak, Mikolaj J.; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions, holding in every dimension. Such a finding constitutes a substantial extension of the one-dimensional bounds deduced in Chatterjee (Ann. Probab. 36 (2008) 1584-1610) and Lachieze-Rey and Peccati (Ann. Appl. Probab. 27 (2017) 1992-2031), as well as of the multidime...
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作者：Onaran, Efe; Bobrowski, Omer; Adler, Robert J.
作者单位：Technion Israel Institute of Technology; University of London; Queen Mary University London
摘要：We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.
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作者：Tanana, Anastasiya
作者单位：University of Texas System; University of Texas Austin
摘要：In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters: the initial wealth and the essential lower bound on consumption process. In order to state the problem and define the primal do-mains, we introduce a natural extension of the notion of running maximum to arbitrary nonnegative optional processes and study its...
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作者：Shapira, Assaf
作者单位：Universite Paris Cite
摘要：This paper concerns with the hydrodynamic limit of the Kob-Andersen model, an interacting particle system that has been introduced by physicists in order to explain glassy behavior, and widely studied since. We will see that the density profile evolves in the hydrodynamic limit according to a nondegenerate hydrodynamic equation, and understand how the diffusion coefficient decays as density grows.
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作者：Alfonsi, Aurelien; Bally, Vlad
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We are concerned with a mixture of Boltzmann and McKean-Vlasov-type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself, and driven by a Poisson point measure with the intensity depending also on the law of the solution. Both the analytical Boltzmann equation and the probabilistic interpretation ini-tiated by Tanaka (Z. Wahrsch. Verw. Gebiete 46 (1978/79) 67-105; J. Fac. Sci., Univ. Tokyo, Sect. IA, Math. 34 (1987) 351-369) hav...
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作者：Bayraktar, Erhan; Deng, Shuoqing; Norgilas, Dominykas
作者单位：University of Michigan System; University of Michigan; Hong Kong University of Science & Technology
摘要：The increasing supermartingale coupling, introduced by Nutz and Stebegg (Ann. Probab. 46 (2018) 3351-3398) is an extreme point of the set of supermartingale couplings between two real probability measures in convex-decreasing order. In the present paper we provide an explicit construction of a triple of functions, on the graph of which the increasing super -martingale coupling concentrates. In particular, we show that the increasing supermartingale coupling can be identified with the left-curt...
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作者：Lehmkuehler, Matthis
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The family of SLE ⠂mu � 4 (-2) exploration processes with parameter mu e R forms a natural class of conformally invariant ways for discovering the loops of a conformal loop ensemble CLE4. Such an exploration consists of one simple continuous path called the trunk of the exploration that discovers CLE4 loops along the way. The parameter mu appears in the Loewner chain description of the path that traces the trunk and all CLE4 loops encountered by the trunk in chronological order. These explor...
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作者：Gheissari, Reza; Sinclair, Alistair
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：It is well known that Glauber dynamics on spin systems typically suffer exponential slowdowns at low temperatures. This is due to the emergence of multiple metastable phases in the state space, separated by narrow bottle-necks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be much faster. However, such phenomena have la...
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作者：Chazottes, Jean-Rene; Gallo, Sandro; Takahashi, Daniel Y.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universidade Federal de Sao Carlos; Universidade Federal do Rio Grande do Norte
摘要：Stochastic chains of unbounded memory (SCUMs) are generalization of Markov chains, also known in the literature as chains with complete con-nections or g-measures. We obtain Gaussian concentration bounds (GCB) in this large class of models, for general alphabets, under two different con-ditions on the kernel: (1) when the sum of its oscillations is less than one, or (2) when the sum of its variations is finite, that is, belongs to l(1)(N). We also obtain explicit constants as functions of the ...
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作者：Anagnostakis, Alexis; Lejay, Antoine; Villemonais, Denis
作者单位：Universite de Lorraine; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and skew behavior. We prove that the convergence occurs at any rate strictly inferior to (1/4) perpendicular to (1/p) in terms of the maximum cell size of the grid, for any p-Wasserstein distance. We also show that it is possible to achieve any rate strictly inf...
