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作者：Budhiraja, Amarjit; Friedlander, Eric; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Chicago; Iowa State University
摘要：The join-the-shortest-queue routing policy is studied in an asymptotic regime where the number of processors n scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as n -> infinity, in a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics with discontinuous statistics, a diminishing rate property of the transition probability rates, and an infinite-dimensional state space. Th...
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作者：Jaramillo, Arturo; Nourdin, Ivan; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We consider empirical processes associated with high-frequency observations of a fractional Brownian motion (fBm) X with Hurst parameter H is an element of (0, 1), and derive conditions under which these processes verify a (possibly uniform) law of large numbers, as well as a second order (possibly uniform) limit theorem. We devote specific emphasis to the zero energy case, corresponding to a kernel whose integral on the real line equals zero. Our asymptotic results are associated with explici...
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作者：Jourdain, Benjamin; Lelievre, Tony; Zitt, Pierre-Andre
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; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables decouples from the dynamics along the other degrees of freedom. We also discuss the bias which is introduced when the adiabatic assumption does not hold.
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作者：Marinucci, Domenico; Rossi, Maurizia; Vidotto, Anna
作者单位：University of Rome Tor Vergata; University of Milano-Bicocca; G d'Annunzio University of Chieti-Pescara
摘要：In this paper, we consider isotropic and stationary real Gaussian random fields defined on S-2 x R and we investigate the asymptotic behavior, as T -> +infinity, of the empirical measure (excursion area) in S-2 x [0, T] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and nonintegrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular...
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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：Introduced by Lu and Yau (Comm. Math. Phys. 156 (1993) 399-433), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance terms has so far precluded applications to heterogeneous models. Here we demonstrate that the existence of an appropriate coupling can be exploited to bypass this limitation effortlessly. Our main result is a dimension-free modifie...
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作者：Broman, Erik, I; Elias, Olof; Mussini, Filipe; Tykesson, Johan
作者单位：Chalmers University of Technology; University of Gothenburg; Uppsala University
摘要：We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition for any dimension d >= 2, and a connectivity phase transition whenever d >= 4. We determine the exact value of the critical point of the existence phase transition, and we show that the fractal set is almost surely empty at this critical point. A key ingredient when analysing the connectivity phase ...
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作者：de Menibus, Benjamin Hellouin; Le Borgne, Yvan
作者单位：Universite Paris Saclay; Universite de Bordeaux
摘要：The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic rock-paper-scissors preypredator relationship. Starting from a random configuration, similar states gather in increasingly large clusters; asymptotically, any finite region is filled with a uniform state that is, after some time, driven out by its predator, each state taking its turn in dominating the region (heteroclinic cycles). We consider the situation where each site in the in...
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作者：Henry-Labordere, Pierre; Touzi, Nizar
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris
摘要：We provide probabilistic representations of the solution of some semi-linear hyperbolic and high-order PDEs based on branching diffusions. These representations pave the way for an approximation of the solution by the standard Monte Carlo method, whose error estimate is controlled by the standard central limit theorem, thus partly bypassing the curse of dimensionality. We illustrate the numerical implications in the context of some popular PDEs in physics such as nonlinear Klein-Gordon equatio...
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作者：Jaber, Eduardo Abi; Miller, Enzo; Pham, Huyen
作者单位：Universite Paris Cite
摘要：We provide an exhaustive treatment of linear-quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite. These equations are in general neither Markovian nor semimartingales, and include the fractional Brownian motion with Hurst index smaller than 1/2 as a special case. We establish the correspondence of the initial problem with a possibly infinite dimension...
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作者：Foutel-Rodier, Felix; Lambert, Amaury; Schertzer, Emmanuel
作者单位：Universite Paris Cite; Sorbonne Universite; Universite PSL; College de France; Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：Kingman's (1978) representation theorem (J. Lond. Math. Soc. (2) 18 (1978) 374-380) states that any exchangeable partition of N can be represented as a paintbox based on a random mass-partition. Similarly, any exchangeable composition (i.e., ordered partition of N) can be represented as a paintbox based on an interval-partition (Gnedin (1997) Ann. Probab. 25 (1997) 1437-1450). Our first main result is that any exchangeable coalescent process (not necessarily Markovian) can be represented as a ...
