On the Poisson Follower Model

dc.contributor.advisorBaccelli, F. (François), 1954-
dc.contributor.committeeMemberDe Veciana, Gustavo
dc.contributor.committeeMemberZitkovic, Gordan
dc.contributor.committeeMemberTran, Ngoc
dc.contributor.committeeMemberTaillefumier, Thibaud O
dc.creatorDragović, Nataša
dc.date.accessioned2021-06-29T02:05:05Z
dc.date.available2021-06-29T02:05:05Z
dc.date.created2020-08
dc.date.issued2020-08-14
dc.date.submittedAugust 2020
dc.date.updated2021-06-29T02:05:06Z
dc.description.abstractThis dissertation presents studies of dynamics over the Poisson point process. In particular, we study a special case of Hegselmann-Krause Dynamics [1] over ℝ². Chapter 1 is a brief introduction to the thesis and its structure. Chapter 2 introduces the notation, the definitions and examples of phenomena of interest. In Chapter 3, we go deeper in analyzing the phenomena described by calculating frequency of these phenomena. A system of quadratic inequalities will be introduced to allow one to calculate the probabilities of the events pertaining to this dynamics using methods from integral geometry. Chapter 4 uses percolation arguments to prove the absence of percolation at step 1. In Chapter 5, we provide geometric results of independent interest pertaining to the Follower Dynamics. In Chapter 6, we discuss the limiting behavior of this process and include some more simulations. In Chapter 7 we propose future steps and discuss more general Hegselmann-Krause Dynamics.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/86699
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/13650
dc.language.isoen
dc.subjectOpinion dynamics
dc.subjectStochastic geometry
dc.subjectPercolation
dc.subjectProbability
dc.subjectDynamical system
dc.titleOn the Poisson Follower Model
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
DRAGOVIC-DISSERTATION-2020.pdf
Size:
2.59 MB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.45 KB
Format:
Plain Text
Description:
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.84 KB
Format:
Plain Text
Description: