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作者：Kim, Seonwoo; Seo, Insuk
作者单位：Korea Institute for Advanced Study (KIAS); Seoul National University (SNU); Seoul National University (SNU)
摘要：The main contribution of the current study is two-fold. First, we investigate the energy landscape of the Ising and Potts models on finite twodimensional lattices without external fields in the low-temperature regime. The complete analysis of the energy landscape of these models was unknown because of its complicated plateau saddle structure between the ground states. We characterize this structure completely in terms of a random walk on the set of subtrees of a ladder graph. Second, we provid...
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作者：Dembin, Barbara; Elboim, Dor; Peled, Ron
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Institute for Advanced Study - USA; Tel Aviv University
摘要：We study first-passage percolation on Z(d), d >= 2, with independent weights whose common distribution is compactly supported in (0,infinity) with a uniformly-positive density. Given & varepsilon;>0 and v is an element of Z(d), which edges have probability at least & varepsilon; to lie on the geodesic between the origin and v? It is expected that all such edges lie at distance at most some r(& varepsilon;)r(& varepsilon;) from either the origin or v, but this remains open in dimensions d >= 3....
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作者：Cerny, Jiri; Drewitz, Alexander; Oswald, Pascal
作者单位：University of Basel; University of Cologne
摘要：We consider one-dimensional branching Brownian motion in a spatially random branching environment (BBMRE) and show that for almost every realisation of the environment, the distributions of the maximal particle of the BBMRE recentred around its median are tight as time evolves. This result is in stark contrast to the fact that the transition fronts in the solution to the randomised Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation are, in general, not bounded uniformly in time. In particu...
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作者：Schapira, Bruno; Valesin, Daniel
作者单位：Aix-Marseille Universite; University of Warwick
摘要：We study the contact process on a dynamic random d-regular graph with an edge-switching mechanism as well as an interacting particle system that arises from the local description of this process called the herds process. Both these processes were introduced in (da Silva, Oliveira and Valesin (2021)); there it was shown that the herds process has a phase transition with respect to the infectivity parameter lambda, depending on the parameter v that governs the edge dynamics. Improving on a resul...
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作者：Benard, Timothee; Breuillard, Emmanuel
作者单位：University of Oxford
摘要：We formulate and establish the central limit theorem for products of i.i.d. random variables on arbitrary simply connected nilpotent Lie groups, allowing a possible bias. We find that some interesting new phenomena arise in the presence of a bias: the walk spreads out at a higher rate in the ambient group, while the limiting hypoelliptic diffusion process may not always have full support. We use elementary Fourier analysis to establish our results, which include Berry-Esseen bounds under optim...
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作者：Crawford, Nicholas; Glazman, Alexander; Harel, Matan; Peled, Ron
作者单位：Technion Israel Institute of Technology; University of Innsbruck; Northeastern University; Tel Aviv University
摘要：The loop O(n) model is a family of probability measures on collections of nonintersecting loops on the hexagonal lattice, parameterized by a loop-weight n and an edge-weight x. Nienhuis predicts that, for 0 < n <2, the model exhibits two regimes separated by xc (n) = 1/2 + root 2 - n: when x < xc(n), the loop lengths have exponential tails, while when x >= xc(n), the loops are macroscopic. In this paper, we prove three results regarding the existence of long loops in the loop O(n) model: - In ...
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作者：Bobkov, Sergey G.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：For normalized sumsZnof i.i.d. random variables, we explore necessaryand sufficient conditions, which guarantee the normal approximation withrespect to the R & eacute;nyi divergence of infinite order. In terms of densitiespnofZn, this is a strengthened variant of the local limit theorem taking the formsupx(pn(x)-phi(x))/phi(x)-> 0asn ->infinity
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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：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.
