Determinantal Processes

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Barzegar, Milad | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49093 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra
Abstract:
Determinantal processes are a special family of stochastic processes that arise in physics (fermions), random matrices (eigenvalues), and in combinatorics (random spanning trees and non-intersecting paths). These processes have repelling property (points close to each other are chosen with low probability). Because of this repelling property, determinantal processes are approporiat for modeling some physical quantities (e.g. the position of electrons). Their probabilistic structure is described by operators on complex vector spaces and their eigenvalues. Determinantal processes have interesting properties, e.g. number of points in a region is a sum of independent Bernoulli random variables. In this thesis we will introduce determinantal processes and investigate their properties. In the end we will use determinantal process to uniformly distribute points on sphere
Keywords:
Point Process ; Discrepancy ; Determinantal Point Processes ; Random Matrix Theory ; Spanning Tree ; Uniform Spanning Tree