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Supporting-points processes and some of their applications
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  • Published: June 2000

Supporting-points processes and some of their applications

  • Y. Baryshnikov1 

Probability Theory and Related Fields volume 117, pages 163–182 (2000)Cite this article

Abstract.

We introduce a stochastic point process of S-supporting points and prove that upon rescaling it converges to a Gaussian field. The notion of S-supporting points specializes (for adequately chosen S) to Pareto (or, more generally, cone) extremal points or to vertices of convex hulls or to centers of generalized Voronoi tessellations in the models of large scale structure of the Universe based on Burgers equation. The central limit theorems proven here imply i.a. the asymptotic normality for the number of convex hull vertices in large Poisson sample from a simple polyhedra or for the number of Pareto (vector extremal) points in Poisson samples with independent coordinates.

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Authors and Affiliations

  1. EURANDOM, Eindhoven Institute of Technology, PB 513, 5600 MB Eindhoven, The Netherlands. e-mail: baryshnikov@eurandom.tue.nl, , , , , , NL

    Y. Baryshnikov

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  1. Y. Baryshnikov
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Received: 20 July 1997 / Revised version: 18 August 1999 /¶Published online: 11 April 2000

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Baryshnikov, Y. Supporting-points processes and some of their applications. Probab Theory Relat Fields 117, 163–182 (2000). https://doi.org/10.1007/s004400050002

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  • Issue Date: June 2000

  • DOI: https://doi.org/10.1007/s004400050002

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Keywords

  • Hull
  • Limit Theorem
  • Convex Hull
  • Extremal Point
  • Central Limit
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