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作者：Lawler, Gregory F.; Werness, Brent M.
作者单位：University of Chicago
摘要：In this paper we define and prove of the existence of the multi-point Green's function for SLE a normalized limit of the probability that an SLE kappa curve passes near to a pair of marked points in the interior of a domain. When kappa <8 this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 14211452]. This work contains a proof of this ...
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作者：Hazra, Rajat Subhra; Maulik, Krishanu
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with regularly varying tails belong to the class of free subexponential distributions. This also shows that the partial sums of free random elements having distributions with regularly varying tails are tail equivalent to their maximum in the sense of Ben Arous and...
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作者：Reitzner, Matthias; Schulte, Matthias
作者单位：University Osnabruck; Helmholtz Association; Karlsruhe Institute of Technology
摘要：A U-statistic of a Poisson point process is defined as the sum Sigma f(x(1),...,x(k)) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-Ito chaos expansion of such a functional is computed and used to derive a formula for the variance. Central limit theorems for U-statistics of Poisson point processes are shown, with explicit bounds for the Wasserstein distance to a Gaussian random variable. As applications, the inter...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Universite de Lorraine
摘要：We prove that an adequately resealed sequence {F-n} of self-adjoint operators, living inside a fixed free Wigner chaos of even order, converges in distribution to a centered free Poisson random variable with rate lambda > 0 if and only if phi(F-n(4)) - 2 phi(F-n(3)) -> 2 lambda(2) - lambda (where phi is the relevant tracial state). This extends to a free setting some recent limit theorems by Nourdin and Peccati [Ann. Probab. 37 (2009) 1412-1426] and provides a noncentral counterpart to a resul...
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作者：Dereich, Steffen; Moerters, Peter
作者单位：University of Munster; University of Bath
摘要：We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We ...
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作者：Bakhtin, Yuri
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also...
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作者：Merlevede, Florence; Peligrad, Magda
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new ...
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作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if (d - 1) tanh beta < 1, then there exists a constant C such that the discrete time mixing time of Gibbs samplers for the ferromagnetic Ising model on any graph of n vertices and maximal degree d, where all interactions are bounded by beta, and arbitrary external fields are bounded by Cn log n. Moreover, the spectral gap is uniformly bounded away from 0 for all such ...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The main results in this paper are about the full coalescence time C of a system of coalescing random walks over a finite graph G. Letting m(G) denote the mean meeting time of two such walkers, we give sufficient conditions under which E[C] approximate to 2m(G) and C/m(G) has approximately the same law as in the mean field setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than m(G); th...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider a random planar map M-n which is uniformly distributed over the class of all rooted q-angulations with n faces. We let m(n) be the vertex set of M-n, which is equipped with the graph distance d(gr). Both when q >= 4 is an even integer and when q = 3, there exists a positive constant c(q) such that the rescaled metric spaces (m(n), c(q)n(-1/4)d(gr)) converge in distribution in the Gromov-Hausdorff sense, toward a universal limit called the Brownian map. The particular case of triang...
