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作者：Hug, D; Reitzner, M; Schneider, R
作者单位：University of Freiburg; Technische Universitat Wien
摘要：In the early 1940s, D. G. Kendall conjectured that the shape of the zero cell of the random tessellation generated by a stationary and isotropic Poisson line process in the plane tends to circularity given that the area of the zero cell tends to infinity. A proof was given by I. N. Kovalenko in 1997. This paper generalizes Kovalenko's result in two directions: to higher dimensions and to not necessarily isotropic stationary Poisson hyperplane processes. In the anisotropic case, the asymptotic ...
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作者：Martin, JB
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We consider directed first-passage and last-passage percolation on the nonnegative lattice Z(+)(d), d greater than or equal to 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = lim(n-->infinity)n(-1)T([nx]) exist and are constant a.s. for x is an element of R-+(d), where T(z) is the passage time from the origin to the vertex z is an element of Z(+)(d). We show that this shape function g is continuous on R-+(d), ...
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作者：Berti, P; Pratelli, L; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A new type of stochastic dependence for a sequence of random variables is introduced and studied. Precisely, (X-n)ngreater than or equal to1 is said to be conditionally identically distributed (c.i.d.), with respect to a filtration (g(n))(ngreater than or equal to0), if it is adapted to (g(n))(ngreater than or equal to0) and, for each ngreater than or equal to0, (X-k)(k>n) is identically distributed given the past g(n). In case g(0) = {theta, Omega} and g(n) = sigma(X-1,...,X-n), a result of K...
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作者：Wu, WB; Woodroofe, M
作者单位：University of Chicago; University of Michigan System; University of Michigan
摘要：Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating martingales satisfy a Lindeberg-Feller condition. Using the explicit construction of the approximating marti...
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作者：Mason, DM
作者单位：University of Delaware
摘要：We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.
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作者：Biskup, M
作者单位：University of California System; University of California Los Angeles
摘要：We consider the (unoriented) long-range percolation on Z(d) in dimensions d greater than or equal to 1, where distinct sites x,y is an element of Z(d) get connected with probability p(xy) is an element of [0, 1]. Assuming p(xy) = \x - y\(-s+o(1)) as \x - y\ --> infinity, where s > 0 and \ (.) \ is a norm distance on Z(d), and supposing that the resulting random graph contains an infinite connected component Cinfinity, we let D(x, y) be the graph distance between x and y measured on Cinfinity. ...
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作者：Strauss, W; Macheras, ND; Musial, K
作者单位：University of Stuttgart; University of Wroclaw
摘要：We prove that if (X, U, P) is an arbitrary probability space with countably generated sigma-algebra U, (Y, B, Q) is an arbitrary complete probability space with a lifting rho and (R) over cap is a complete probability measure on Ucircle times(R) B determined by a regular conditional probability {S-y : y is an element of Y} on U with respect to B, then there exist a lifting pi on (X x Y, Ucircle times(R) B, (R) over cap) and liftings sigma(y) on (X, (U) over cap (y), (S) over cap (y)), y is an ...
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作者：Bahadoran, C
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider an arbitrary one-dimensional conservative particle system with finite-range interactions and finite site capacity, governed on the hydrodynamic scale by a scalar conservation law with Lipschitz-continuous flux h. A finite-size perturbation restricts the local current to some maximum value phi. We show that the perturbed hydrodynamic behavior is entirely determined by phi if inf(h; phi) is first nondecreasing and then nonincreasing, which we believe is a necessary condition.
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作者：Bardet, JB; Ben Arous, GR
作者单位：Universite Paris Nanterre; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider the (d + 1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on Z(d) together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this ...
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作者：Engländer, J; Kyprianou, AE
作者单位：University of California System; University of California Santa Barbara; Utrecht University
摘要：Let X be either the branching diffusion corresponding to the operator Lu + beta(u(2) - u) on D subset of or equal to R-d [where beta(x) greater than or equal to 0 and beta not equivalent to 0 is bounded from above] or the superprocess corresponding to the operator Lu + betau - alphau(2) on D subset of or equal to R-d (with alpha > 0 and beta is bounded from above but no restriction on its sign). Let lambda(c) denote the generalized principal eigenvalue for the operator L + beta on D. We prove ...
