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作者：Nachmias, Asaf; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 denote the largest connected component of the critical Erdos-Renyi random graph G(n, 1/n). We show that, typically, the diameter of C-1 is of order n(1/3) and the mixing time of the lazy simple random walk on C-1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald. These results extend to clusters of size n(2/3) of p-bond percolation on any d-regular n-vertex graph where such clusters exist, provided that p(d-1) <= 1 + O(n(-1/3)).
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in R-n that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on D boolean AND 2(-k)Z(n) moving at the rate 2(-2k) with stationary initial distribution converge weakly in the space D([0, 1], R-n), equipped with the Skor...
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作者：Dolgopyat, Dmitry; Koralov, Leonid
作者单位：University System of Maryland; University of Maryland College Park
摘要：We consider a process oil 72, which consists of fast motion along the stream lines of ail incompressible periodic vector field perturbed by white noise. It gives rise to a process on the graph naturally associated to the structure of the stream lines Of the unperturbed flow. It has been shown by Freidlin and Wentzell [Random Perturbations of Dynamical Systems, 2nd ed. Springer. New York (1998)] and [Mem. Amer Math. Soc. 109 (1994)] that if the stream function of the flow is periodic. then the ...
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作者：Ma, Jin; Zhang, Jianfeng; Zheng, Ziyu
作者单位：University of Southern California
摘要：In this paper, we propose a new notion of Forward-Backward Martingale, Problem (FBMP), and study its relationship with the weak solution to the forward-backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan. but it is structured specifically to fit the nature of an FBSDE. We first prove a general sufficient condition for the existence of the solution to the FBMP. In the Markovian case with uniformly ...
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作者：Helton, J. William; Lasserre, Jean B.; Putinar, Mihai
作者单位：University of California System; University of California San Diego; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Santa Barbara
摘要：We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure mu has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain conditional triangularity property of the orthogonal polynomials associated with mu.
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作者：Hagg, Jonas
作者单位：Royal Institute of Technology
摘要：We prove that the Airy process, A(t), locally fluctuates like a Brownian motion. In the same spirit we also show that, in a certain scaling limit, the so-called discrete polynuclear growth process (PNG) behaves like a Brownian motion.
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Let xi be a Dawson-Watanabe superprocess in R-d such that xi(t) is a.s. locally finite for every t >= 0. Then for d >= 2 and fixed t > 0. the singular random measure xi(t) can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the epsilon-neighborhoods of supp xi(t). When d >= 3. the local distributions of xi(t) near a hitting point can be approximated in total variation by those of a stationary and self-similar pseudo-random measure by contrast, the corresponding ...
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作者：Schreiber, T.; Yukich, J. E.
作者单位：Nicolaus Copernicus University; Lehigh University
摘要：We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sample. The approach involves introducing a generalized spatial birth growth process allowing for cell ove...
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作者：Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of ...
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance Must be bounded has an explicit formula that makes it possible to carry out the program more easily. As an application, we derive a general CLT for functions that are obtained as combinations of many local contributions,...
