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作者：Kim, Ildoo; Kim, Kyeong-Hun; Lim, Sungbin
作者单位：Korea University
摘要：In this article, we present an L-p-theory (p >= 2) for the semi-linear stochastic partial differential equations (SPDEs) of type partial derivative(alpha)(t)u = L(omega,t,x)u + f(u) + partial derivative(beta)(t) Sigma(infinity)(k=1)integral(t)(0)(Lambda(k)(omega,t,x)u + g(k)(u)) dw(t)(k), where alpha is an element of (0,2), beta < alpha + 1/2 and partial derivative(alpha)(t) and partial derivative(beta)(t) denote the Caputo derivatives of order alpha and beta, respectively. The processes omega...
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作者：Bourguin, Solesne; Campese, Simon; Leonenko, Nikolai; Taqqu, Murad S.
作者单位：Boston University; University of Luxembourg; Cardiff University
摘要：We obtain quantitative four moments theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. These results are obtained by first proving a general carre du champ bound on the distance between laws of random variables in the domain of a Markov diffusion generator and invariant measures of diffusions, which is of independent interest, and making use of the n...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general method for lower bounds on fluctuations. The method is used to obtain new results for the stochastic traveling salesman problem, the stochastic minimal matching problem, the random assignment problem, the Sherrington-Kirkpatrick model of spin glasses, first-pa...
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作者：Gwynne, Ewain; Miller, Jason
作者单位：Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：In a recent series of works, Miller and Sheffield constructed a metric on root 8/3-Liouville quantum gravity (LQG) under which root 8/3-LQG surfaces (e.g., the LQG sphere, wedge, cone and disk) are isometric to their Brownian surface counterparts (e.g., the Brownian map, half-plane, plane and disk). We identify the metric gluings of certain collections of independent root 8/3-LQG surfaces with boundaries identified together according to LQG length along their boundaries. Our results imply in p...
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作者：Sert, Cagri
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Under a Zariski density assumption, we extend the classical theorem of Cramer on large deviations of sums of i.i.d. real random variables to random matrix products.
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作者：Birkner, Matthias; Sun, Rongfeng
作者单位：Johannes Gutenberg University of Mainz; National University of Singapore
摘要：The lonely branching random walks on Z(d) is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. We show that if the symmetrized walk is recurrent, lonely branching random walks die out locally. Further-more, the same result holds if additional branching is allowed when the walk is not alone.
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作者：Bobkov, S. G.; Chistyakov, G. P.; Goerzet, F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：We explore properties of the chi(2) and Renyi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).
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作者：Shao, Qi-Man; Zhang, Zhuo-Song
作者单位：Chinese University of Hong Kong
摘要：An exchangeable pair approach is commonly taken in the normal and nonnormal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the difference of the exchangeable pair is not bounded by a small deterministic constant, the error bound is often not optimal. In this paper, using the exchangeable pair approach of Stein's method, a new Berry-Esseen bound for an arbitrary random variable is estab...
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作者：Senizergues, Delphin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13
摘要：We construct random metric spaces by gluing together an infinite sequence of pointed metric spaces that we call blocks. At each step, we glue the next block to the structure constructed so far by randomly choosing a point on the structure and then identifying it with the distinguished point of the block. The random object that we study is the completion of the structure that we obtain after an infinite number of steps. In (Ann. Inst. Fourier (Grenoble) 67 (2017) 1963-2001), Curien and Haas stu...
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作者：Chong, Carsten; Kevei, Peter
作者单位：Technical University of Munich; Technical University of Munich; Szeged University
摘要：We investigate the moment asymptotics of the solution to the stochastic heat equation driven by a (d + 1)-dimensional Levy space-time white noise. Unlike the case of Gaussian noise, the solution typically has no finite moments of order 1 + 2/d or higher. Intermittency of order p, that is, the exponential growth of the pth moment as time tends to infinity, is established in dimension d = 1 for all values p is an element of (1, 3), and in higher dimensions for some p is an element of (1, 1 2/d)....
