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作者：Atar, Rami; Cohen, Asaf
作者单位：Technion Israel Institute of Technology; University of Michigan System; University of Michigan
摘要：A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time horizon [0, T] is considered. The main result is the asymptotic optimality of a control policy derived via an underlying differential game. The result is the first to address a queueing control problem at the moderate deviation regime that goes beyond models ...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：We consider disordered systems of a directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2 + 1), the long-range directed polymer model with Cauchy tails in dimension (1 + 1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field ...
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作者：Mossel, Elchanan; Roch, Sebastien
作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of the distribution and a sparse signal. Using this connection, we derive an information-theoretic trade-off between the number of genes, m, needed for an accurate reconstruction and the sequence length, k, of the genes. Specifically, we show that to detect a b...
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作者：Sly, Allan; Zhang, Yumeng
作者单位：Australian National University; University of California System; University of California Berkeley
摘要：The mixing time of the Glauber dynamics for spin systems on trees is closely related to the reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding the log-Sobolev constant by a comparison with the block dynamics [ Comm. Math. Phys. 250 (2004) 301-334; Random Structures Algorithms 31 (2007) 134-172]. However, when there are hard constraints, the dynamics inside blocks may be reducible. We introduce a vari...
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作者：Doering, Leif; Klenke, Achim; Mytnik, Leonid
作者单位：University of Mannheim; Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here, we show convergence of the so-called finite system scheme for interacting jump-type processes known as mutually catalytic branching processes with infinite branching rate. Due to the lack of second moments, the rescaling of time is different from the finite rate mutually catalytic case. The limit of rescaled total mass processes is id...
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作者：Hambly, Ben; Ledger, Sean
作者单位：University of Oxford; University of Bristol
摘要：We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes large, the empirical measure of the population converges to the solution of a nonlinear stochastic heat equation with Dirichlet boundary condition. The diffusion coefficients are allowed to have finitely many discontinuities (piecewise Lipschitz) and we prov...
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作者：Benaim, Michel; Bouguet, Florian; Cloez, Bertrand
作者单位：University of Neuchatel; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier; Universite de Lorraine; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro
摘要：In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the...
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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：Dondl, Patrick W.; Scheutzow, Michael
作者单位：University of Freiburg; Technical University of Berlin
摘要：We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a d-dimensional lattice coupled by the discrete Laplacian. At each lattice point, the system is subject to a constant driving force and a random obstacle force impeding free propagation. The obstacle force depends on the current state of the solution, and thus renders the pro...
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作者：Etheridge, Alison; Freeman, Nic; Penington, Sarah; Straulino, Daniel
作者单位：University of Oxford; University of Sheffield
摘要：We ask the question when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population? We focus on the situation in which neighbourhood size, that is the effective local population density, is small. The genealogy relating individuals in a sample from the population is embedded in a spatial version of the ancestral selection graph and through applying a diffusive scaling to this objec...
