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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 ...
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作者：Lawler, GF; Schramm, O; Werner, W
作者单位：Cornell University; Universite Paris Saclay; Microsoft
摘要：This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain D (subset of)(not equal) C is equal to the radial SLE2 path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that partial derivativeD is a C-1-simple closed curve, the same method is applied to show that the scaling limit of the uniform spanning tree Peano ...
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作者：Li, WV; Shao, QM
作者单位：University of Delaware; University of Oregon
摘要：Let X = (X-t)(tis an element ofS) be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(sup(tis an element ofS)(X-t - X-t0) less than or equal to x) as x --> 0, with t(0) is an element of S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities...
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作者：Wang, FY
作者单位：Beijing Normal University
摘要：By using probabilistic approaches, some uniform gradient estimates are obtained for Dirichlet heat semigroups on a Riemannian manifold with boundary. As an application, lower bound estimates of isoperimetric constants are presented in terms of functional inequalities.
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作者：Fukushima, M; He, P; Ying, JG
作者单位：Kansai University; Shanghai University of Finance & Economics; Fudan University
摘要：We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.
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作者：Djellout, H; Guillin, A; Wu, L
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Wuhan University
摘要：We first give a characterization of the L-1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.
