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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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Randomized integer convex hull

Hong Ngoc, Binh 12 February 2021 (has links)
The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables.
lattice polytopes
lattice-free
intrinsic volumes
mixed multiplicities
Bhattacharya function
Newton polyhedron
complete monomial ideals
mean width
random lattices
integer convex hull
random polytopes
31.70 - Wahrscheinlichkeitsrechnung
31.23 - Ideale, Ringe, Moduln, Algebren
13-02 - Research exposition
ddc:510

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