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作者：Castiel, Eyal; Borst, Sem; Miclo, Laurent; Simatos, Florian; Whiting, Phil
作者单位：Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Eindhoven University of Technology; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Macquarie University
摘要：We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the N/N-2 scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from th...
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作者：van der Hofstad, Remco; van Leeuwaarden, Johan S. H.; Stegehuis, Clara
作者单位：Eindhoven University of Technology; Tilburg University; University of Twente
摘要：Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a subgraph or as an induced subgraph. We obtain these results by analyzing the configuration model with degree exponent tau epsilon (2, 3) and introducing a novel class of optimization problems. For any given subgraph, the unique optimizer describes the degrees of t...
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作者：Hirsch, Christian; Holmes, Mark; Kleptsyn, Victor
作者单位：University of Groningen; University of Melbourne; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a vertex fires, one of the edges incident to that vertex is selected. The edge selection is biased towards edges that have been selected many times previously, and a parameter a governs the strength of this bias. We show that for various graphs (including all graphs of bounded degree), if alpha >> 1 (the very strong reinforcement regime) then the random subgraph consisting of...
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作者：Nejjar, Peter
作者单位：University of Bonn
摘要：We consider the asymmetric simple exclusion process (ASEP) on Z with initial data such that in the large time particle density rho(.) a discontinuity (shock) at the origin is created. At the shock, the value of rho jumps from zero to one, but rho(-epsilon), 1 - rho(epsilon) > 0 for any epsilon > 0. We are interested in the rescaled position of a tagged particle which enters the shock with positive probability. We show that, inside the shock region, the particle position has the KPZ-typical 1/3...
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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：Introduced by Lu and Yau (Comm. Math. Phys. 156 (1993) 399-433), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance terms has so far precluded applications to heterogeneous models. Here we demonstrate that the existence of an appropriate coupling can be exploited to bypass this limitation effortlessly. Our main result is a dimension-free modifie...
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作者：Szpruch, Lukasz; Tse, Alvin
作者单位：University of Edinburgh
摘要：Let mu is an element of P-2(R-d), where P-2(R-d) denotes the space of square integrable probability measures, and consider a Borel-measurable function Phi : P-2(R-d) -> R. In this paper we develop an antithetic Monte Carlo estimator (A-MLMC) for Phi(mu), which achieves sharp error bound under mild regularity assumptions. The estimator takes as input the empirical laws mu(N) = 1/N Sigma(N)(i =1) delta X-i, where (a) (X-i)(i =1)(N) is a sequence of i.i.d. samples from mu or (b) (X-i)(i =1)(N) is...
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作者：Altmeyer, Randolf; Reiss, Markus
作者单位：Humboldt University of Berlin
摘要：The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space. For the asymptotic regime with fixed time horizon and with the spatial resolution of the observations tending to zero, we provide rate-optimal estimators and establish scaling limits of the deterministic PDE and of the SPDE on growing domains. The estimators...
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作者：Dembo, Amir; Lubetzky, Eyal; Zeitouni, Ofer
作者单位：Stanford University; Stanford University; New York University; Weizmann Institute of Science
摘要：We study dynamics for asymmetric spin glass models, proposed by Hertz et al. and Sompolinsky et al. in the 1980's in the context of neural networks: particles evolve via a modified Langevin dynamics for the Sherrington-Kirkpatrick model with soft spins, whereby the disorder is i.i.d. standard Gaussian rather than symmetric. Ben Arous and Guionnet (Probab. Theory Related Fields 102 (1995) 455-509), followed by Guionnet (Probab. Theory Related Fields 109 (1997) 183-215), proved for Gaussian inte...
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作者：Broman, Erik, I; Elias, Olof; Mussini, Filipe; Tykesson, Johan
作者单位：Chalmers University of Technology; University of Gothenburg; Uppsala University
摘要：We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition for any dimension d >= 2, and a connectivity phase transition whenever d >= 4. We determine the exact value of the critical point of the existence phase transition, and we show that the fractal set is almost surely empty at this critical point. A key ingredient when analysing the connectivity phase ...
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作者：Bate, Michael E.; Connor, Stephen B.; Matheau-Raven, Oliver
作者单位：University of York - UK
摘要：We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric group generated by a distribution which is nonconstant on the conjugacy class of transpositions. Nevertheless, we provide an explicit formula for all eigenvalues of the shuffle by demonstrating a useful correspondence between eigenvalues and standard Young ...
