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作者：Davis, Erik; Sethuraman, Sunder
作者单位：University of Arizona
摘要：Given a graph, the popular modularity clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this paper, we discuss scaling limits of this method with respect to random geometric graphs constructed from i.i.d. points X-n = {X-1, X-2,..., X-n}, distributed according to a probability measure nu supported on a bounded domain D subset of R-d. Among other results, we show, via a Gamma convergence framework, a geometric form of consistency: Wh...
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作者：Fountoulakis, Nikolaos; Mueller, Tobias
作者单位：University of Birmingham; Utrecht University; University of Groningen
摘要：We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are associated with so-called complex networks. The model is controlled by two parameters alpha and nu where, roughly speaking, alpha controls the exponent of the power law and nu controls the average degree. Refining earlier results, we are able to show a law of large ...
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作者：Sasada, Makiko
作者单位：University of Tokyo
摘要：In the diffusive hydrodynamic limit for a symmetric interacting particle system (such as the exclusion process, the zero range process, the stochastic Ginzburg-Landau model, the energy exchange model), a possibly nonlinear diffusion equation is derived as the hydrodynamic equation. The bulk diffusion coefficient of the limiting equation is given by the Green-Kubo formula and it can be characterized by a variational formula. In the case the system satisfies the gradient condition, the variation...
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作者：Litvak, Alexander E.; Tikhomirov, Konstantin
作者单位：University of Alberta; University of Alberta; Princeton University
摘要：Let X be an n-dimensional random centered Gaussian vector with independent but not identically distributed coordinates and let T be an orthogonal transformation of R-n. We show that the random vector Y = T (X) satisfies E Sigma j=1(k) j-min (i)(<= n) X-i(2 )<= CE Sigma j=1(k) j-min(i)(<= n) Y-i(2 ) for all k <= n, where j-min denotes the jth smallest component of corresponding vector and C >0 is a universal constant. This resolves (up to a multiplicative constant) an old question of S. Mallat ...
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作者：Blanchard, Romain; Carassu, Laurence
作者单位：Universite de Reims Champagne-Ardenne
摘要：This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.
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作者：Cheek, David; Antal, Tibor
作者单位：University of Edinburgh
摘要：First, we revisit the stochastic Luria-Delbruck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously ...
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作者：Shneer, Seva; Stolyar, Alexander
作者单位：Heriot Watt University; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated-ach node receives an exogenous flow of packets at the rate of. packets per time slot. Each packet takes one slot to transmit, but neighbouring nodes cannot transmit simultaneously. The algorithm we study is standard in the following sense: a node with an empty queue does not compete f...
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作者：Bally, Vlad; Goreac, Dan; Rabiet, Victor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel
摘要：We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann equation, piecewise deterministic Markov processes, etc.). First, we give sufficient conditions guaranteeing that the semigroup associated with such an equation preserves regularity by mapping the space of k-times differentiable bounded functions into itself. Furt...
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作者：Bjornberg, Jakob E.; Ueltschi, Daniel
作者单位：Chalmers University of Technology; University of Gothenburg; University of Warwick
摘要：We give estimates of the critical parameter for random loop models that are related to quantum spin systems. A special case of the model that we consider is the interchange- or random-stirring process. We consider here the model defined on regular trees of large degrees, which are expected to approximate high spatial dimensions. We find a critical parameter that indeed shares similarity with existing numerical results for the cubic lattice. In the case of the interchange process, our results i...
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作者：Deligiannidis, George; Lee, Anthony
作者单位：University of Oxford; University of Warwick; University of Bristol; Alan Turing Institute
摘要：We show that the class of L-2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L-2 functions for which ergodic averages of its associated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple sufficient con...
