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作者：Arlotto, Alessandro; Steele, J. Michael
作者单位：Duke University; University of Pennsylvania
摘要：We construct a stationary ergodic process X-1, X-2,... such that each X-t has the uniform distribution on the unit square and the length Ln of the shortest path through the points X-1, X-2,, X-n is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley [Proc. Cambridge Philos. Soc. 55 (1959) 299-327] theorem does not extend from the case of independent uniformly distributed random variables to the case of stationary ergodic s...
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作者：Bertoin, Jean; Kortchemski, Igor
作者单位：University of Zurich
摘要：We are interested in the asymptotic behavior of Markov chains on the set of positive integers for which, loosely speaking, large jumps are rare and occur at a rate that behaves like a negative power of the current state, and such that small positive and negative steps of the chain roughly compensate each other. If X-n is such a Markov chain started at n, we establish a limit theorem for 1/n X-n appropriately scaled in time, where the scaling limit is given by a nonnegative self-similar Markov ...
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作者：McKeague, Ian W.; Levin, Bruce
作者单位：Columbia University
摘要：From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical worlds. The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Phys. R...
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作者：Diehl, Joscha; Friz, Peter; Mai, Hilmar
作者单位：Technical University of Berlin; University of California System; University of California San Diego; Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise stability properties as well as robustness toward misspecification in volatility and even the very nature of the noise. Two numerical examples demonstrate the practical relevance of our results.
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作者：Corwin, Ivan; Liu, Zhipeng; Wang, Dong
作者单位：Columbia University; Sorbonne Universite; Massachusetts Institute of Technology (MIT); New York University; National University of Singapore
摘要：We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general down-right lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar...
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作者：Jia, Chen; Jiang, Da-Quan; Qian, Min-Ping
作者单位：Chinese Academy of Engineering Physics; Beijing Computational Science Research Center (CSRC); Peking University; Peking University
摘要：In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov chains. Moreover, we use these cycle symmetries to study the circulation fluctuations for Markov chains. We prove that the sample circulations along a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has a highly nonobvious symmetry. Further extensions and appli...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Sorbonne Universite
摘要：We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the q-Hahn TASEP and the q-Hahn Boson (zero-range) process introduced in [J. Phys. A 46 (2013) 465205, 25] and further studied in [Int. Math. Res. Not. IMRN 14 (2015) 5577-5603], by allowing jumps in both directions. Owing to a Markov duality, we prove moment formulas for the locations of particles in the exclusion process. This leads to a Fredholm determinant formula that characterize...
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作者：Mossel, Elchanan; Neeman, Joe; Sly, Allan
作者单位：University of Pennsylvania; University of California System; University of California Berkeley; University of Bonn; University of Texas System; University of Texas Austin; Australian National University
摘要：We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a/n and b/n for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better than a random guess if and only if (a - b)(2) > 2(a b). Using a variant of belief propagation, we give a reconstruction algorithm that is optimal in the sense that if (a - b)(2) > C (a b) for some constant C then our algorithm maximizes the fraction of the nodes ...
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作者：Douc, Randal; Roueff, Francois; Sim, Tepmony
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the equivalence class of the true parameter, which is a key feature for obtaining the consistency of the maximum likelihood estimators (MLEs) in well-specified models. This result is obtained in the general framework of partially dominated models. We examine two s...
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作者：Torrisi, Giovanni Luca
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.
