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作者：Goldsheid, Ilya; Sodin, Sasha
作者单位：University of London; Queen Mary University London; Tel Aviv University
摘要：The eigenvalues of the Hatano-Nelson non-Hermitian Anderson matrices, in the spectral regions in which the Lyapunov exponent exceeds the non-Hermiticity parameter, are shown to be real and exponentially close to the Hermitian eigenvalues. This complements previous results, according to which the eigenvalues in the spectral regions in which the non-Hermiticity parameter exceeds the Lyapunov exponent are aligned on curves in the complex plane.
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作者：Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Columbia University; Duke University; Duke University; City University of Hong Kong
摘要：Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare-event analysis for such elliptic PDEs with random inputs. In particular, we consider the asymptotic regime that the noise level converges to zero suggesting that the system uncertainty is low, but does exist. We develop sharp approximations of the probability of a larg...
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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
摘要：The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure v using a random sample of size n drawn from a different probability measure If the two measures mu and v are nearly singular with respect to each other, which is often the case in practice, the sample size required for accurate estimation is large. In this article, it is shown that in a fairly general setting, a sample of size approximately exp(D(v || mu)) is necessary a...
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作者：Federico, Salvatore; Gozzi, Fausto
作者单位：University of Siena; Luiss Guido Carli University
摘要：Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper, we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal control problems. The method applies in the case of additively controlled Ornstein-Uhlenbeck processes, when the associated Hamilton-Jacobi-Bellman (HJB) equation admits a mild solution (in the sense of [J. Differential Equations 262 (2017) 3343-3389]). The m...
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作者：Avena, Luca; Guldas, Hakan; van der Hofstad, Remco; den Hollander, Frank
作者单位：Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on n vertices, is known to be of order log n. In this paper, we investigate what happens when the random graph becomes dynamic, namely, at each unit of time a fraction alpha(n) of the edges is randomly rewired. Under mild conditions on the degree sequence, guaranteeing that the graph is locally tree-like, we show that for every epsilon is an element of (0, 1) the eps...
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作者：Casanova, Adrian Gonzalez; Spano, Dario
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Warwick
摘要：A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals first choose a (random) number of potential parents from the previous generation and then, from the selected pool, they inherit the type of the fittest parent. The probability distribution function of the number of potential parents per individual thus parame...
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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：Bobrowski, Omer; Kahle, Matthew; Skraba, Primoz
作者单位：Duke University; University System of Ohio; Ohio State University; Slovenian Academy of Sciences & Arts (SASA); Jozef Stefan Institute; University of Primorska; Technion Israel Institute of Technology
摘要：We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-k in persistent homology, for a either the Cech or the Vietoris-Rips filtration built on a uniform Poisson process of intensity n in the unit cube [0, 1](d). This is a natural way of measuring the largest k-dimensional hole in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally ...
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作者：Burzoni, Matte; Frittelli, Marco; Maggis, Marco
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Milan
摘要：In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path omega is an element of Omega, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analy...
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作者：Bierkens, Joris; Roberts, Gareth
作者单位：Delft University of Technology; University of Warwick
摘要：In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis Hastings (LMH). A scaling limit of the magnetization process in the Curie Weiss model is derived for LMH, as well as for Metropolis Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n(1/2) for LMH, which should be compared to n for MH. At the critical temp...
