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作者：Pang, Guodong; Pardoux, Etienne
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of infection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these m...
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作者：Alberts, Tom; Normand, Raoul
作者单位：Utah System of Higher Education; University of Utah; New York University
摘要：We study the dimension properties of the spectral measure of the circular beta-ensembles. For beta >= 2 it was previously shown by Simon that the spec-tral measure is almost surely singular continuous with respect to Lebesgue measure on partial differential D and the dimension of its support is 1 - 2/beta. We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emp...
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作者：Kumar, Chaman; Neelima; Reisinger, Christoph; Stockinger, Wolfgang
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Oxford
摘要：In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients of super-linear growth in the state variable. Second, we present stable time-stepping schemes for this class of McKean-Vlasov SDEs. Specifically, we propose an explicit tamed Euler and tamed Milstein scheme for an interacting particle system associated with the McKean-Vlasov equation. We prove stability and strong convergence of ...
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作者：Yao, Jianfeng; Yuan, Wangjun
作者单位：The Chinese University of Hong Kong, Shenzhen; University of Hong Kong
摘要：In this article, we establish a limiting distribution for eigenvalues of a class of autocovariance matrices. The same distribution has been found in the literature for a regularized version of these autocovariance matrices. The original nonregularized autocovariance matrices are noninvertible, thus introducing supplementary difficulties for the study of their eigenvalues through Girko's Hermitization scheme. The key result in this paper is a new polynomial lower bound for a specific family of ...
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作者：Bakhtin, Yuri; Chen, Hong-Bin; Pajor-Gyulai, Zsolt
作者单位：New York University
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作者：Banerjee, Sayan; Bhamidi, Shankar
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider models of growing random trees {T-f (n) : n >= 1} with model dynamics driven by an attachment function f : Z(+) -> R+. At each stage a new vertex enters the system and connects to a vertex v in the current tree with probability proportional to f (degree(v)). The main goal of this study is to understand the performance of root finding algorithms. A large body of work (e.g., Random Structures Algorithms 50 (2017) 158-172; IEEE Trans. Netw. Sci. Eng. 4 (2017) 1-12; Random Structures A...
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作者：Forien, Raphael; Pardoux, Etienne
作者单位：INRAE; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：This paper presents a new view of household epidemic models, where we exploit the fact that the interaction between the households is of mean field type. We prove the convergence, as the number of households tends to infinity, of the number of infectious individuals in a uniformly chosen household to a nonlinear Markov process solving a McKean-Vlasov Poisson driven stochastic differential equation, as well as a propagation of chaos result. We also define a basic reproduction number R-* and sho...
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作者：Butez, Raphael; Garcia-Zelada, David
作者单位：University of Geneva; Aix-Marseille Universite
摘要：We study the outliers for two models which have an interesting connection. On the one hand, we study a specific class of planar Coulomb gases which are determinantal. It corresponds to the case where the confining potential is the logarithmic potential of a radial probability measure. On the other hand, we study the zeros of random polynomials that appear to be closely related to the first model. Their behavior far from the origin is shown to depend only on the decaying properties of the proba...
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作者：Bierkens, Joris; Kamatani, Kengo; Roberts, Gareth O.
作者单位：Delft University of Technology; University of Osaka; University of Warwick
摘要：Piecewise deterministic Markov processes are an important new tool in the design of Markov chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy particle sampler (BPS) and the zig-zag process (ZZ). In this paper scaling limits for both algorithms are determined. Here the dimensionality of the space tends towards infinity and the target distribution is the multivariate standard normal distribution. For several quantities of interest (angular momentum, first coordin...
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作者：Basdevant, Anne-Laure; Gouere, Jean-Baptiste; Theret, Marie
作者单位：Universite de Tours
摘要：We consider the standard model of first-passage percolation on Z(d) (d >= 2), with i.i.d. passage times associated with either the edges or the vertices of the graph. We focus on the particular case where the distribution of the passage times is the Bernoulli distribution with parameter 1 - epsilon. These passage times induce a random pseudo-metric T-epsilon on R-d. By subadditive arguments, it is well known that for any z is an element of R-d \ {0}, the sequence T-epsilon(0, nz)/n converges a...
