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作者：El Karoui, Nicole; Loisel, Stephane; Salhi, Yahia
作者单位：Sorbonne Universite; Universite Claude Bernard Lyon 1
摘要：We consider the minimax quickest detection problem of an unobservable time of proportional change in the intensity of a doubly-stochastic Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. This problem, introduced by Page [Biometrika 41 (1954) 100-115], has received more attention in the continuous path framework (for Wiener processes) tha...
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作者：Lachieze-Rey, Raphael; Peccati, Giovanni
作者单位：Universite Paris Cite; University of Luxembourg
摘要：We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of nonlinear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference operators, and generalise the bounds obtained by Chatter-jee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a n...
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The presence of frozen-in or quenched disorder in a system can often modify the nature of its phase transition. A particular instance of this phenomenon is the so-called rounding effect: it has been shown in many cases that the free energy curve of the disordered system at its critical point is smoother than that of the homogeneous one. In particular some disordered systems do not allow first-order transitions. We study this phenomenon for the pinning of a renewal with stretched-exponential ta...
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作者：Nguyen, Hoi H.
作者单位：University System of Ohio; Ohio State University
摘要：Suppose that A(1),..., A(N) are independent random matrices of size n whose entries are i.i.d. copies of a random variable xi of mean zero and variance one. It is known from the late 1980s that when xi is Gaussian then N-1 log parallel to A(N)... A(1) parallel to converges to log root n as N -> 8. We will establish similar results for more general matrices with explicit rate of convergence. Our method relies on a simple interplay between additive structures and growth of matrices.
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作者：Laslier, Benoit; Laslier, Jean-Francois
作者单位：Universite Paris Cite; Paris School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：This paper deals with two generalizations of the Polya urn model where, instead of sampling one ball from the urn at each time, we sample two or three balls. The processes are defined on the basis of the problem of finding the best alternative using pairwise comparisons which are not necessarily transitive: they can be thought of as evolutionary processes that tend to reinforce currently efficient alternatives. The two processes exhibit different behaviors: with three balls sampled, we prove a...
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作者：He, Yukun; Knowles, Antti
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.
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作者：Belomestny, Denis; Kraetschmer, Volker
作者单位：University of Duisburg Essen; HSE University (National Research University Higher School of Economics)
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作者：Feige, Uriel; Krivelevich, Michael; Reichman, Daniel
作者单位：Weizmann Institute of Science; Tel Aviv University; University of California System; University of California Berkeley
摘要：We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, r) be the minimal size of a contagious set. We study this process on the binomial random graph G := G(n, p) with p := d/n and 1 << d << (nloglogn/log(2)n )(r-1/r). Assuming r > 1 to...
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作者：Fournier, Nicolas; Jourdain, Benjamin
作者单位：Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Gustave-Eiffel
摘要：We are interested in the two-dimensional Keller-Segel partial differential equation. This equation is a model for chemotaxis (and for Newtonian gravitational interaction). When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity chi of bacteria to the chemo-attractant is larger than 8 pi. We investigate its approximation by a system of N two-dimensional Brownian particles interacting through a singular attractive kernel in the ...
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作者：Grigorova, Miryana; Imkeller, Peter; Offen, Elias; Ouknine, Youssef; Quenez, Marie-Claire
作者单位：Humboldt University of Berlin; University of Botswana; Cadi Ayyad University of Marrakech; Universite Paris Cite
摘要：In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate Banach spaces. The result is established by using some results from optimal stopping theory, some tools from the general theory of processes such as Mertens' decomposition of optional strong supermartingale...
