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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.
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作者：Baake, Ellen; Cordero, Fernando; Hummel, Sebastian
作者单位：University of Bielefeld
摘要：We consider the mutation-selection differential equation with pairwise interaction (or, equivalently, the diploid mutation-selection equation) and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph. The formal relation to the forward model is given via duality. To make the tree tractable, we prune branches upon mutations, thus reducing it to its informative parts. The hierarchies inherent in the tree are encoded systematically v...
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作者：Banerjee, Sayan; Budhiraja, Amarjit; Puha, Amber L.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; California State University System; California State University San Marcos
摘要：We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. Since one needs to keep track of the remaining processing times of all jobs in the system in order to describe the evolution, a natural state descriptor for an SRPT queue is a measure valued process in which the state of the system at a given time is the finite nonnegative Borel measure...
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
摘要：It was shown in (J. Amer. Math. Soc. 24 (2011) 919-944) that the edge of the spectrum of beta ensembles converges in the large N limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature 1/beta goes to infinity: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on R of intensity ex dx and that the eigenfunctions converge t...
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作者：Chen, Hong-Bin
作者单位：New York University
摘要：We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of the two vectors are only assumed to have scaled bounded supports. We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the ...
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作者：Chassagneux, Jean-Francois; Szpruch, Lukasz; Tse, Alvin
作者单位：Universite Paris Cite; University of Edinburgh
摘要：Consider the metric space (P-2(R-d), W-2) of square integrable laws on R-d with the topology induced by the 2-Wasserstein distance W-2. Let Phi : P-2(R-d) -> R and mu is an element of P-2(R-d). In this work, we consider (a) mu(N) being the empirical measure of N-samples from mu, and the other case in which (b) mu(N) is the empirical measure of marginal laws of the particle system of a McKean-Vlasov PDE (mu(t))(t). The main result of this paper is to show that under suitable regularity conditio...
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作者：Bandyopadhyay, Antar; Thacker, Debleena
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; Durham University
摘要：In this work, we introduce a generalization of the classical Polya urn scheme (Ann. Inst. Henri Poincare 1 (1930) 117-161) with colors indexed by a Polish space, say, S. The urns are defined as finite measures on S endowed with the Borel sigma-algebra, say, S. The generalization is an extension of a model introduced earlier by Blackwell and MacQueen (Ann. Statist. 1 (1973) 353-355). We present a novel approach of representing the observed sequence of colors from such a scheme in terms an assoc...
