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作者：Bhattacharjee, Chinmoy; Schulte, Matthias
作者单位：University of Luxembourg; Hamburg University of Technology
摘要：We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet. We achieve this by proving convergence of the underlying point process of the degrees to a certain Poisson process. Estimating the index of the power-law tail for the typical degree distribution is an important question in statistics. We prove consistency o...
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作者：Louart, Cosme; Couillet, Romain
作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：This article studies the robust covariance matrix estimation of a data collection X = (x1, ... , xn) with xi = /tau izi + m, where zi is an element of Rp is a con-centrated vector (e.g., an elliptical random vector), m is an element of Rp a deterministic signal and tau i is an element of R a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called s...
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作者：Penda, S. Valere Bitseki; Delmas, Jean-Francois
作者单位：Universite Bourgogne Europe; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (Ann. ...
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作者：Broutin, Nicolas; Duquesne, Thomas; Wang, Minmin
作者单位：Universite Paris Cite; Sorbonne Universite; University of Sussex
摘要：Motivated by limits of critical inhomogeneous random graphs, we construct a family of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the multiplicative coalescent (the Erdos-Renyi random graph, more generally the so-called rank-one inhomogeneous random graphs of various types, and the configuration model). At the discrete level, the construction relies on a new point of view on (discrete) inhomogeneous rand...
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作者：Bouchard, Bruno; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Chinese University of Hong Kong
摘要：We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (SIAM J. Control Optim. 57 (2019) 4125-49), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explici...
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作者：Curato, Imma Valentina; Stelzer, Robert; Stroeh, Bennet
作者单位：Ulm University
摘要：We obtain central limit theorems for stationary random fields employing a novel measure of dependence called theta-lex weak dependence. We show that this dependence notion is more general than strong mixing, that is, it applies to a broader class of models. Moreover, we discuss hereditary properties for theta-lex and eta-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general resu...
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作者：Fu, Yingjia; Williams, Ruth J.
作者单位：University of California System; University of California San Diego
摘要：This work concerns the asymptotic behavior of solutions to a critical fluid model for a data communication network, where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy, chosen from the family of (weighted) alpha-fair policies introduced by Mo and Walrand (IEEE/ACM Trans. Netw. 8 (2000) 556-567). Solutions of the fluid model are measure-valued functions of time. Under law of large numbers scaling, Gromoll and Williams (Ann. Appl. Probab. 19 ...
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作者：Coppini, Fabio
作者单位：Universite Paris Cite
摘要：The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit deterministic condition on the sequence of graphs such that, for any finite time and any initial condition, even dependent on the network, the empirical measure of the system stays close to the solution of the McKean-Vlasov equation associated to the classical m...
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作者：Foucart, Clement
摘要：We consider the class of exchangeable fragmentation-coagulation (EFC) processes where coagulations are multiple and not simultaneous, as in a Lambda-coalescent, and fragmentation dislocates at a finite rate an individual block into sub-blocks of infinite size. We call these partition-valued processes simple EFC processes, and study the question whether such a process, when started with infinitely many blocks, can visit partitions with a finite number of blocks or not. When this occurs, one say...
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作者：Li, Xue-Mei; Sieber, Julian
作者单位：Imperial College London
摘要：We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Holder norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.
