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作者：Lalley, Steven; Su, Wei
作者单位：University of Chicago
摘要：We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the cutoff phenomenon in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any epsilon > 0, when the number n of vertices is large then (a) at times t < (C - epsilon) log n the fraction of ...
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作者：Leobacher, Gunther; Szolgyenyi, Michaela
作者单位：University of Graz; Vienna University of Economics & Business; Johannes Kepler University Linz; Vienna University of Economics & Business
摘要：In this paper, we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method that converges with strong order 1/2. Our result is the first one that shows existence and uniqueness as well as strong convergence for such a general class of SDEs. The proof is based on a transformation technique that removes the disconti...
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作者：Chatterjee, Sourav; Sen, Sanchayan
作者单位：Stanford University; McGill University
摘要：Kesten and Lee [Ann. AppL Probab. 6 (1996) 495-527] proved that the total length of a minimal spanning tree on certain random point configurations in R-d satisfies a central limit theorem. They also raised the question: how to make these results quantitative? Error estimates in central limit theorems satisfied by many other standard functionals studied in geometric probability are known, but techniques employed to tackle the problem for those functionals do not apply directly to the minimal sp...
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作者：Ghiglietti, Andrea; Vidyashankar, Anand N.; Rosenberger, William F.
作者单位：University of Milan; George Mason University
摘要：The generalized Polya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with a diagonal replacement matrix, which arise in several applications, specifically in clinical trials. To facilitate mathematical analyses of models in these applications, we introduce an adaptive randomly reinforced urn model that uses accruing statistical information to adaptively skew the urn proportio...
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作者：Bierme, Hermine; Durieu, Olivier; Wang, Yizao
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; University of Cincinnati
摘要：Recently, Hammond and Sheffield [Probab. Theory Related Fields 157 (2013) 691-719] introduced a model of correlated one-dimensional random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension d >= 2. We define a Z(d)-indexed random field with dependence relations governed by an underlying random graph with vertices Z(d), and we study the scaling limits of the partial sums of the random field o...
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作者：Dommers, S.; Den Hollander, F.; Jovanovski, O.; Nardi, F. R.
作者单位：Ruhr University Bochum; Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：In this paper, we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the configuration model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferro-magnetic pair potential. We start from th...
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作者：Bou-Rabee, Nawaf; Maria Sanz-Serna, Jesus
作者单位：Rutgers University System; Rutgers University Camden; Universidad Carlos III de Madrid
摘要：Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory way. In this article, we present and analyze a randomized HMC method (RHMC), in which these durations are i.i.d. exponential random variables whose mean is a free parameter. We focus on the small time step size limit, where the algorithm is rejection-free an...
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作者：Costantini, Cristina; De Blasi, Pierpaolo; Ethier, Stewart N.; Ruggiero, Matteo; Spano, Dario
作者单位：G d'Annunzio University of Chieti-Pescara; University of Turin; Utah System of Higher Education; University of Utah; University of Warwick
摘要：The two-parameter Poisson-Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming-Viot processes. The additional parameter has been shown to regulate the clustering structure of the population, but is yet to be fully understood in the way it governs the reproductive process. Here, we shed some light on these dynamics by formulating a K-allele Wright-F...
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作者：Fischer, Markus
作者单位：University of Padua
摘要：Mean field games are limit models for symmetric N-player games with interaction of mean field type as N -> infinity. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate Nash equilibria for the corresponding N-player games. The opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean field game? In this direction, rigorous results are mostly available for stationa...
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作者：Laruelle, Sophie; Pages, Gilles
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 Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
