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作者：Jin, Ke
作者单位：University of Delaware
摘要：The Mallows measure is a probability measure on S-n where the probability of a permutation pi is proportional to q(l(pi)) with q > 0 being a parameter and l(pi) the number of inversions in pi. We prove a weak law of large numbers for the length of the longest common subsequences of two independent permutations drawn from the Mallows measure, when q is a function of n and n(1 - q) has limit in R as n ->infinity.
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作者：Burdzy, Krzysztof; Gauthier, Carl-Erik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero, properly rescaled angular component of the light ray position converges in distribution to a diffusion whose parameters (diffusivity and drift) are given explicitly in terms of the tube width.
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作者：Kloeckner, Benoit
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Applying quantitative perturbation theory for linear operators, we prove nonasymptotic bounds for Markov chains whose transition kernel has a spectral gap in an arbitrary Banach algebra of functions X. The main results are concentration inequalities and Berry-Esseen bounds, obtained assuming neither reversibility nor warm start hypothesis: the law of the first term of the chain can be arbitrary. The spectral gap hypothesis is basically a uniform X - ergodicity hypothesis, and when X consist in...
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作者：Wang, Andi Q.; Kolb, Martin; Roberts, Gareth O.; Steinsaltz, David
作者单位：University of Oxford; University of Paderborn; University of Warwick
摘要：This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein-Uhlenbeck process with Gaussian quasi-stationary d...
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作者：Keller-Ressel, Martin; Schmidt, Thorsten; Wardenga, Robert
作者单位：Technische Universitat Dresden; University of Freiburg; University of Freiburg
摘要：In this paper, we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting, times of jumps can be both inaccessible and predictable. To this end, we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equation...
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作者：Hammond, Alan; Hegde, Milind
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study a spatial model of random permutations on trees with a time parameter T > 0, a special case of which is the random stirring process. The model on trees was first analysed by Bjornberg and Ueltschi [Ann. Appl. Probab. 28 (2018) 2063-2082], who established the existence of infinite cycles for T slightly above a putatively identified critical value but left open behaviour at arbitrarily high values of T. We show the existence of infinite cycles for all T greater than a constant, thus cla...
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作者：Szpruch, Lukasz; Tan, Shuren; Tse, Alvin
作者单位：University of Edinburgh
摘要：The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean (Proc. Natl. Acad. Sci. USA 56 (1966) 1907-1911) as they pave a way to probabilistic representations for many important nonlinear/nonlocal PDEs. The fact that particles are not independent render classical variance reduction techniques not directly applicable, and consequently make simulations of interacting diffusions prohibitive. I...
