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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：Given an instance of the preferential attachment graph G(n) = ([n], E-n), we would like to find vertex 1, using only local information about the graph; that is, by exploring the neighborhoods of small sets of vertices. Borgs et al. gave an algorithm which runs in time O(log(4) n), which is local in the sense that at each step, it needs only to search the neighborhood of a set of vertices of size O(log(4) n). We give an algorithm to find vertex 1, which w.h.p. runs in time O (omega log n) and w...
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作者：Baar, Martina; Bovier, Anton; Champagnat, Nicolas
作者单位：University of Bonn; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a model for Darwinian evolution in an asexual population with a large but nonconstant populations size characterized by a natural birth rate, a logistic death rate modeling competition and a probability of mutation at each birth event. In the present paper, we study the long-term behavior of the system in the limit of large population (K -> infinity) size, rare mutations (u -> 0) and small mutational effects (sigma -> 0), proving convergence to the canonical equation of adaptive dy...
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作者：Fricker, Christine; Tibi, Danielle
作者单位：Universite Paris Cite
摘要：For a class of large closed Jackson networks submitted to capacity constraints, asymptotic independence of the nodes in normal traffic phase is proved at stationarity under mild assumptions, using a local limit theorem. The limiting distributions of the queues are explicit. In the Statistical Mechanics terminology, the equivalence of ensembles-canonical and grand canonical-is proved for specific marginals. The framework includes the case of networks with two types of nodes: single server/finit...
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作者：van den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study a percolation model on the square lattice, where clusters freeze (stop growing) as soon as their volume (i.e., the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in van den Berg, de Lima and Nolin [Random Structures Algorithms 40 (2012) 220-226] and Kiss [Probab. Theory Related Fields 163 (2015) 713-768]. Using volume as a way to measure the size of a cluster instead of diamete...
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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.
