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作者：Matoussi, Anis; Stoica, Lucretiu
作者单位：Le Mans Universite; Romanian Academy; University of Bucharest; Institute of Mathematics of the Romanian Academy; University of Bucharest
摘要：We prove an existence and uniqueness result for the obstacle problem of quasi linear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation.
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作者：Hu, Xiaoyu; Miller, Jason; Peres, Yuval
作者单位：Chinese Academy of Sciences; Stanford University; Microsoft
摘要：Let U subset of C be a bounded domain with smooth boundary and let F be an instance of the continuum Gaussian free field on U with respect to the Dirichlet inner product integral(U) del f(x).del g(x)dx. The set T (a; U) of a-thick points of F consists of those z is an element of U such that the average of F on a disk of radius r centered at z has growth root a/pi log 1/r as r -> 0. We show that for each 0 <= a <= 2 the Hausdorff dimension of T (a; U) is almost surely 2 - a, that nu(2-a)(T (a; ...
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作者：Bollobas, Bela; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver
作者单位：University of Cambridge; University of Memphis; Microsoft; University of Oxford
摘要：In this paper we determine the percolation threshold for an arbitrary sequence of dense graphs (G(n)). Let lambda(n) be the largest eigenvalue of the adjacency matrix of G(n), and let G(n)(p(n)) be the random subgraph of G(n) obtained by keeping each edge independently with probability p(n). We show that the appearance of a giant component in G(n)(P-n) has a sharp threshold at p(n) = 1/lambda(n). In fact, we prove much more: if (G(n)) converges to an irreducible limit, then the density of the ...
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作者：Boutillier, Cedric; de Tiliere, Beatrice
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; University of Neuchatel
摘要：The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero and the aspect of the torus is fixed, the winding number of the collection of loops converges in law to a two-dimensional discrete Gaussian distribution. This is known to physicists in more generality from their analysis of toroidal two-dimensional critical...
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作者：Chen, Zhen-Qing; Zhang, Tusheng
作者单位：University of Washington; University of Washington Seattle; University of Manchester
摘要：In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.
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作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut; University of Cambridge
摘要：Let p(n)(y) = Sigma(k)(alpha) over cap (k)phi(y - k) + Sigma(jn-1)(l=0) Sigma(k)(beta) over cap (lk)2(l/2)psi(2(l) y-k) be the linear wavelet density estimator, where phi, psi are a father and a mother wavelet (with compact support), (alpha) over cap (k), (beta) over cap (lk) are the empirical wavelet coefficients based on an i.i.d. sample of random variables distributed according to a density p(0) on R, and j(n) is an element of Z, j(n) NE arrow infinity. Several uniform limit theorems are pr...
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作者：Evans, Steven N.
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic behavior as n -> infinity of the spectra of random matrices of the form 1/root n-1 (n-1)Sigma(k=1) Z(nk)rho(n) ((k, k + 1)), where for each n the random variables Z(nk) are i.i.d. standard Gaussian and the matrices rho(n) ((k, k + 1)) are obtained by applying an irreducible unitary representation rho(n) of the symmetric group on {1, 2,...,n} to the transposition (k, k + 1) that interchanges k and k + 1 [thus, rho(n) ((k, k + 1)) is both unitary and self-adjoint, with...
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作者：Dubins, Lester E.; Gilat, David; Meilijson, Isaac
作者单位：University of California System; University of California Berkeley; Tel Aviv University
摘要：It is shown that the ratio between the expected diameter of an L-2-bounded martingale and the standard deviation of its last term cannot exceed root 3. Moreover, I one-parameter family of stopping times on standard Brownian motion is exhibited, for which the root 3 upper bound is attained. These stopping times, one for each cost-rate c, are optimal when the payoff for stopping at time t is the diameter D(t) obtained up to time t minus the hitherto accumulated cost ct. A quantity related to dia...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Saclay
摘要：We show how to detect optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and the method of moments and cumulants, and provide de facto local (one-term) Edgeworth expansions. The findings of the present paper represent a further refinement of the main results proven in Nourdin and Peccati [Probab. Theory Related Fields 145 (2009) 75-118]. Among several examples, we discuss thr...
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作者：Tudor, Ciprian A.; Viens, Frederi G.
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H > 1/2, we show the remarkable fact that the process's data at time 1 can be used ...
