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作者：Mukherjee, Chiranjib; Varadhan, S. R. S.
摘要：In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential tightness estimate is needed to establish it. In dealing with the occupation measure L-t(A) = 1/t integral(t)(0) 1(A)(W-s) ds of the d-dimensional Brownian motion, which is not positive recurrent, there is no possibility of exponential tightness. The space of ...
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作者：Ortgiese, Marcel; Roberts, Matthew I.
作者单位：University of Munster; University of Bath
摘要：We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an application we show that the branching random walk is intermittent, in the sense that most particles are concentrated on one very small island with large potential. Moreover, we compare the branching random walk to the parabolic Anderson model and observe that al...
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作者：Harris, S. C.; Hesse, M.; Kyprianou, A. E.
作者单位：University of Bath; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0, K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the proc...
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作者：Cai, Chunhao; Chigansky, Pavel; Kleptsyna, Marina
作者单位：Nankai University; Hebrew University of Jerusalem; Le Mans Universite
摘要：This paper presents a new approach to the analysis of mixed processes X-t = B-t + G(t), t is an element of [0, T] where B-t is a Brownian motion and G(t) is an independent centered Gaussian process. We obtain a new canonical innovation representation of X, using linear filtering theory. When the kernel K(s,t) = partial derivative(2)/partial derivative s partial derivative t EG(t)G(s,) s not equal t has a weak singularity on the diagonal, our results generalize the classical innovation formulas...
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作者：Bierme, Hermine; Desolneux, Agnes
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：In this paper, we use the framework of functions of bounded variation and the coarea formula to give an explicit computation for the expectation of the perimeter of excursion sets of shot noise random fields in dimension n >= 1. This will then allow us to derive the asymptotic behavior of these mean perimeters as the intensity of the underlying homogeneous Poisson point process goes to infinity. In particular, we show that two cases occur: we have a Gaussian asymptotic behavior when the kernel...
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作者：Ben Arous, Gerard; Cabezas, Manuel; Cerny, Jiri; Royfman, Roman
作者单位：New York University; University of Vienna
摘要：We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on Z. These scaling limits include the well-known fractional kinetics process, the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call spatially subordinated Brownian motions. We give sufficient conditions for convergence and illustrate these on two important examples.
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作者：Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Jilin University; University System of Georgia; Georgia Institute of Technology
摘要：We consider a Fokker-Planck equation in a general domain in R-n with L-loc(p) drift term and W-loc(1,p) diffusion term for any p > n. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit be...
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作者：Romik, Dan; Sniady, Piotr
作者单位：University of California System; University of California Davis; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Wroclaw
摘要：We study an infinite version of the jeu de taquin sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson Schensted Knuth (RSK) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variable...
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作者：Viklund, Fredrik Johansson
作者单位：Uppsala University
摘要：We estimate convergence rates for curves generated by Loewner's differential equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is what we call the tip structure modulus, a geometric measure of regularity for Loewner curves parameterized by capacity. It is analogous to Warschawski's boundary structure modulus and closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approachi...
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作者：Le Gall, Jean-Francois; Lin, Shen
作者单位：Universite Paris Saclay
摘要：We study the range R-n, of a random walk on the d-dimensional lattice Z(d) indexed by a random tree with n vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension d <= 3 that n(-d/4)R(n) converges in distribution to the Lebesgue measure of the support of the integrated super-Brownian excursion (ISE). An auxiliary result shows that the suitably rescaled local times of the tree-indexed random walk converge in distribution to the densit...
