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作者：Schilling, RL
作者单位：Nottingham Trent University; Universite Paris Saclay
摘要：Let (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C-c(infinity)(R-n) subset of D(A) and A\C-c(infinity)(R-n) is a pseudo-differential operator with symbol -p(x,xi) satisfying parallel to p(.,xi parallel to(infinity) less than or equal to c(1 + parallel to xi parallel to(2)) and \Im p(x,xi)\ less than or equal to c(0) Re p(x,xi). We show that the associated Feller process {X-t}(t greater than or equal to 0) on R-n is a semimartingale, even a homogeneous diffusion with ...
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作者：Talagrand, M
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Ohio State University
摘要：Consider 0 < alpha < 1 and the Gaussian process Y(t) on R-N with covariance E(Y(s)Y(t)) = \t\(2 alpha) + \s\(2 alpha) - \t - s\(2 alpha), where \t\ is the Euclidean norm of t. Consider independent copies X-1,...,X-d of Y and the process X(t) = (X-1(t),...,X-d(t)) valued in R-d. When kN less than or equal to (k - 1)alpha d, we show that the trajectories of X do not have k-multiple points. If N < alpha d and kN > (k - 1)alpha d, the set of k-multiple points of the trajectories X is a countable u...
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作者：Benjamini, I; Schramm, O
作者单位：Weizmann Institute of Science
摘要：Consider the standard continuous percolation in IR4, and choose the parameters so that the induced percolation on a fixed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.
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作者：Toubol, A
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris Cite
摘要：Comets and Neveu have initiated in [5] a method to prove convergence of the partition function of disordered systems to a lognormal random variable in the high temperature regime by means of stochastic calculus. We generalize their approach to a multidimensional Sherrington-Kirkpatrick model with an application to the Heisenberg model of uniform spins on a sphere of R-d, see [9]. The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical en...
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作者：Cekanavicius, V
作者单位：Vilnius University
摘要：For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets. Asymptotics can be constructed two-ways: by adding summands to the leading term or by adding summands in its exponent. The choice of approximations is confirmed by the Ibragimov-type necessary and sufficient conditions.
