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作者：Dekking, FM; von der Wal, P
作者单位：Delft University of Technology
摘要：Branching cellular automata (BCA) are introduced as generalisations of fractal percolation by admitting neighbour dependence. We associate sequences of random sets with BCA's and study their convergence. In case of convergence we derive the Hausdorff dimension of the limit set and of its boundary. To accomplish the latter we proof that the boundary of a set generated by a BCA is again a set generated by a BCA.
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作者：Léandre, R
作者单位：Universite de Lorraine
摘要：We define a stochastic cohomology theory related to a stochastic diffeology for the Hoelder loop space. We show that the stochastic de Rham cohomology groups are equal to the deterministic de Rham cohomology groups of the Hoelder loop space. As an application, we show that a stochastic line bundle over the Brownian bridge (with fiber almost surely defined) is isomorphic to a true line bundle over the Hoelder loop space.
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作者：Mörters, P
作者单位：University of Kaiserslautern
摘要：In this paper we investigate fast particles in the range and support of super-Brownian motion in the historical setting. In this setting each particle of super-Brownian motion alive at time t is represented by a path w : [0, t] --> R-d and the state of historical super-Brownian motion is a measure on the set of paths. Typical particles have Brownian paths, however in the uncountable collection of particles in the range of a super-Brownian motion there are some which at exceptional times move f...
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作者：Talagrand, M
作者单位：Sorbonne Universite; University System of Ohio; Ohio State University
摘要：We study the Hopfield model at temperature 1, when the number M(N) of patterns grows a bit slower than N. We reach a good understanding of the model whenever M(N) less than or equal to N/(log N)(11). For example, we show that if M(N) --> infinity, for two typical configurations sigma (1), sigma (2), (Sigma (i less than or equal toN)sigma (1)(i)sigma (2)(i))(2) is close to NM(N).
