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• Survival and extinction in a locally regulated population AI翻译
  作者：Etheridge, AM
  作者单位：University of Oxford
  摘要：Bolker and Pacala recently introduced a model of an evolving population in which an individual's fecundity is reduced in proportion to the local population density. We consider two versions of this model and prove complementary extinction/persistence results, one for each version. Roughly, if individuals in the population disperse sufficiently quickly relative to the range of the interaction induced by the density dependent regulation, then the population has positive chance of survival, where...
• A general limit theorem for recursive algorithms and combinatorial structures AI翻译
  作者：Neininger, R; Rüschendorf, L
  作者单位：McGill University; University of Freiburg
  摘要：Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structure and the asymptotics of the first and second moments of the sequence. In particular, a general asym...
• Approximation of smooth convex bodies by random circumscribed polytopes AI翻译
  作者：Boroczky, K; Reitzner, M
  作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Freiburg
  摘要：Choose n independent random points on the boundary of a convex body K subset of R-d. The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n --> infinity are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best ...
• Limit theorems for random normalized distortion AI翻译
  作者：Cohort, P
  作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
  摘要：We present some convergence results about the distortion D-mu,n,r(v) related to the Voronoi vector quantization of a mu-distributed random variable using n i.i.d. v-distributed codes. A weak law of large numbers for n(r/d)D(mu,n,r)(v) is derived essentially under a mu-integrability condition on a negative power of a delta-lower Radon-Nikodym derivative of v. Assuming in addition that the probability measure mu has a bounded epsilon-potential, we obtain a strong law of large numbers for n(r/d)D...