Loading...

**Search for:**determinantal-point-processes

0.005 seconds

#### The spherical ensemble and uniform distribution of points on the sphere

, Article Electronic Journal of Probability ; Volume 20 , 2015 , 23, 27 pp ; 10836489 (ISSN) ; Zamani, M ; Sharif University of Technology
University of Washington
2015

Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on $2. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this paper we study the spherical ensemble and its local repelling property by investigating the...

#### Irregularities of Some Random Point Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

The spherical ensemble is a well-studied determinantal process with a fixed number of points on the sphere. The points of this process correspond to the generalized eigenvalues of two appropriately chosen random matrices, mapped to the surface of the sphere by stereographic projection. This model can be considered as a spherical analogue for other random matrix models on the unit circle and complex plane such as the circular unitary ensemble or the Ginibre ensemble, and is one of the most natural constructions of a (statistically) rotation invariant point process with repelling property on the sphere. In this dissertation we study the spherical ensemble and its local repelling property by...

#### Determinantal Processes

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
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....