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作者：Dussaule, Matthieu; Wang, Longmin; Yang, Wenyuan
作者单位：Universite d'Angers; Nankai University; Peking University
摘要：Let Gamma be a nonelementary, relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure mu on Gamma and a probability measure nu on N with mean r. Let BRW(Gamma, nu, mu) be the branching random walk on Gamma with offspring distribution v and base motion given by the random walk with step distribution mu. It is known that, for 1 < r <= R with R the radius of convergence for the Green function of the random walk, the popu...
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作者：Benaim, Michel; Champagnat, Nicolas; Ocafrain, William; Villemonais, Denis
作者单位：University of Neuchatel; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Inria; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France
摘要：We investigate quasi-stationarity properties of Feller processes that are killed when exiting a relatively compact set. Our main result provides general conditions ensuring that such a process possesses a (possibly nonunique) quasi-stationary distribution. Conditions ensuring uniqueness and exponential convergence are discussed. Our conditions are well suited to the study of degenerate processes, such as nonelliptic diffusions or piecewise deterministic Markov processes (PDMP). The results are...
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作者：LE Gall, JEAN-FRANcOIS; Perkins, Edwin
作者单位：Universite Paris Saclay; University of British Columbia
摘要：We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both excursion theory for the Brownian snake and tools from the theory of superprocesses.
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作者：Das, Sayan; Liao, Yuchen; Mucciconi, Matteo
作者单位：Columbia University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore
摘要：In this paper we study large time large deviations for the height function h(x, t) of the q-deformed polynuclear growth introduced in (Int. Math. Res. Not. IMRN 7 (2023) 5728-5780). We show that the upper-tail deviations have speed t and derive an explicit formula for the rate function Phi+(mu). On the other hand, we show that the lower-tail deviations have speed t2 and express the corresponding rate function Phi-(mu) in terms of a variational problem. Our analysis relies on distributional ide...
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作者：Qin, Shuo
作者单位：New York University
摘要：We prove a conjecture by Bertoin that the multidimensional elephant random walk on Zd is transient in dimensions d >= 3. We show that it undergoes a phase transition in dimensions d = 1, 2 between recurrence and transience at p = (2d + 1)/(4d).
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作者：Tunk, Stefan
作者单位：Gakushuin University
摘要：We study the directed polymer model in a bounded environment in weak disorder without L2-boundedness, specifically the speed of homogenization for the field (Wnx)xEZd, where Wnxdenotes the associated martingale for the polymer starting from x. We show that a suitably recentered spatial average over a set of diameter n1/2 convergence to zero at rate n-xi+o(1), where the exponent is an explicit function of the inverse temperature beta.
