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作者：Chen, Xinxin; He, Hui
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Beijing Normal University
摘要：Given a branching random walk on R started from the origin, where the tail of the branching law decays at least exponentially fast and the offspring number is at least one, let Z(n)(.) be the counting measure which counts the number of individuals at the n-th generation located in a given set. Under some mild conditions, it is known (Biggins in Stoch. Process. Appl. 34:255-274, 1990) that for any interval A subset of R, Z(n)(root nA)/Z(n)(R) converges a.s. to nu(A), where nu is the standard Ga...
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作者：Dembo, Amir; Huang, Ruojun; Zheng, Tianyi
作者单位：Stanford University; Stanford University; University of California System; University of California San Diego
摘要：For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks evolving via time varying, uniformly elliptic conductances, provided the vertex conductances (i.e. reversing measures), increase in time. Such transition density upper bounds apply for discrete time uniformly lazy walks, with the matching lower bounds holding once ...
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作者：Buckingham, Robert; Liechty, Karl
作者单位：DePaul University; University System of Ohio; University of Cincinnati
摘要：The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson sea on the unit circle with drift. For any k is an element of Z, we show that an appropriate double scaling of the drift and return time leads to a generalization of the tacnode process in which k particles are expected to wrap around the circle. We derive ...
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作者：Freidlin, Mark; Koralov, Leonid; Wentzell, Alexander
作者单位：University System of Maryland; University of Maryland College Park; Tulane University
摘要：We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a diffusion on the space where each of the pockets is treated as a single point, and certain conditions on the behavior of the process on the boundary of the pockets are imposed. Calculation of various probabilities and expectations related to the limiting process...
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作者：Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.
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作者：Conforti, Giovanni
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：The Schrodinger problem is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schrodinger as the problem of describing the most likely evolution of a large number of Brownian particles conditioned to reach an unexpected configuration. Its optimal value, the entropic transportation cost, and its optimal solution, the Schrodinger bridge, stand as the natural probabilistic counterparts to the transportation cost and...
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作者：Dahlqvist, Antoine; Diehl, Joscha; Driver, Bruce K.
作者单位：University College Dublin; Max Planck Society; University of California System; University of California San Diego
摘要：We show well-posedness for the parabolic Anderson model on 2-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order.
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作者：Ott, Sebastien; Velenik, Yvan
作者单位：University of Geneva
摘要：We consider finite-range ferromagnetic Ising models on Z(d) in the regime beta < beta(c). We analyze the behavior of the prefactor to the exponential decay of Cov(sigma(A), sigma(B)), for arbitrary finite sets A and B of even cardinality, as the distance between A and B diverges.
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作者：Bordenave, Charles; Caputo, Pietro; Salez, Justin
作者单位：Roma Tre University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Cite; Universite Paris Cite
摘要：We study convergence to equilibrium for a class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix P the mass is essentially concentrated on few entries. Moreover, the entries are exchangeable within each row. This includes various models of random walks on sparse random directed graphs. The models are generally non reversible and the equilibrium distribution is itself unknown. In this general setting we establish the cutoff ph...
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作者：Boyer, Jean-Baptiste
作者单位：Universite Paris Saclay
摘要：Let be a probability measure on :=SLd(Z). Consider the random walk defined by on the torus Td=Rd/Zd: for any xTd, the walk starting at x is defined by where (gn)N is chosen with the law circle times N. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an assumption on the group generated by the support of , the random walk starting at any irrational point equidistributes in the torus. In this article, we study the Functional Central Limit Theorem and the almost sure Functional Centr...
