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作者：Samorodnitsky, Gennady; Wang, Yizao
作者单位：Cornell University; University System of Ohio; University of Cincinnati
摘要：We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one regime, our results exhibit limits that are not among the classical extreme value distributions. Restricted to the one-dimensional case, the distributions we obtain interpolate, in the appropriate parameter range, the alpha-Frechet distribution and the skew...
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作者：Etheridge, Alison M.; Kurtz, Thomas G.
作者单位：University of Oxford; University of Wisconsin System; University of Wisconsin Madison
摘要：Representations of population models in terms of countable systems of particles are constructed, in which each particle has a type, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, lambda], whereas in the infinite intensity limit lambda -> infinity, at each time t, the joint distribution of types and levels is conditionally Poisson, with mean measure Xi(t) x l where l denotes Lebesgue measure and Xi(t) is a ...
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作者：Labbe, Cyril; Lacoin, Hubert
作者单位：Universite PSL; Universite Paris-Dauphine; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL
摘要：We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our results show that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic comparisons and concentration inequalities.
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作者：Aggarwal, Amol; Borodin, Alexei
作者单位：Harvard University; Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：In this paper, we consider two models in the Kardar-Parisi-Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call shape generalized step Bernoulli initial data) for both of these models that generalizes the step Bernoulli initial data studied in a number of recent works on the ASEP. Under this class of initial data, we analyze the current fluctuations of both the ASEP and stocha...
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作者：Blaszczyszyn, B.; Yogeshwaran, D.; Yukich, J. E.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Lehigh University
摘要：Let P be a simple, stationary point process on R d having fast decay of correlations, that is, its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let P-n := P boolean AND W-n be its restriction to windows W-n := [- 1/2n(1/2), 1/2n(1/d)](d) subset of R-d. We consider the statistic := E-n(xi) := Sigma(x is an element of Pn) xi (x, P-n) where xi(x, P-n) denotes a score function representing the interaction of x with respect to P-...
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作者：Thalmaier, Anton; Thompson, James
作者单位：University of Luxembourg
摘要：For a semigroup P-t generated by an elliptic operator on a smooth mani-fold M, we use straightforward martingale arguments to derive probabilistic formulae for P-t (V(f)), not involving derivatives of f, where V is a vector field on M. For nonsymmetric generators, such formulae correspond to the derivative of the heat kernel in the forward variable. As an application, these formulae can be used to derive various shift-Hamack inequalities.
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作者：Cass, Thomas; Lim, Nengli
作者单位：Imperial College London; Singapore University of Technology & Design
摘要：Given a Gaussian process X, its canonical geometric rough path lift X, and a solution Y to the rough differential equation (RDE) dY(t) = V (Y-t) circle dX(t), we present a closed-form correction formula for integral Y circle dX - integral Y dX, that is, the difference between the rough and Skorohod integrals of Y with respect to X. When X is standard Brownian motion, we recover the classical Stratonovich-to-Ito conversion formula, which we generalize to Gaussian rough paths with finite p-varia...
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作者：Rhee, Chang-Han; Blanchet, Jose; Zwart, Bert
作者单位：Northwestern University
摘要：Let X be a Levy process with regularly varying Levy measure v. We obtain sample-path large deviations for scaled processes (X) over bar (n) (t) (sic) X (nt)/n and obtain a similar result for random walks with regularly varying increments. Our results yield detailed asymptotic estimates in scenarios where multiple big jumps in the increment are required to make a rare event happen; we illustrate this through detailed conditional limit theorems. In addition, we investigate connections with the c...
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作者：Patie, Pierre; Savov, Mladen; Zhao, Yixuan
作者单位：Cornell University; Bulgarian Academy of Sciences
摘要：In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of Ito, of these semigroups satisfy the same intertwining identity. Under mild additional assumptions on the intertwining operator, we prove that the converse also holds. This connection, which relies on the representation of excursion quantities as developed by Fitzsimmons and Getoor (Illinois J. Math. 50 (2006...
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作者：Soo, Terry; Wilkens, Amanda
作者单位：University of Kansas
摘要：As part of a general theory for the isomorphism problem for actions of amenable groups, Ornstein and Weiss (J. Anal. Math. 48 (1987) 1-141) proved that any two Poisson point processes are isomorphic as measure-preserving actions. We give an elementary construction of an isomorphism between Poisson point processes that is finitary.
