Title:	Randomized integer convex hull
Authors:	Hong Ngoc, Binh
Thesis advisor:	Prof. Dr. Matthias Reitzner
Thesis referee:	Prof. Dr. Ngo Viet Trung
Abstract:	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.
URL:	https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202102124020
Subject Keywords:	lattice polytopes; lattice-free; intrinsic volumes; mixed multiplicities; Bhattacharya function; Newton polyhedron; complete monomial ideals; mean width; random lattices; integer convex hull; random polytopes
Issue Date:	12-Feb-2021
License name:	Attribution-NonCommercial-ShareAlike 4.0 International
License url:	http://creativecommons.org/licenses/by-nc-sa/4.0/
Type of publication:	Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:	FB06 - E-Dissertationen

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