Coupling and unimodularity in stationary settings

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dc.contributor.advisorBaccelli, F. (François), 1954-
dc.contributor.committeeMemberBowen, Lewis
dc.contributor.committeeMemberSadun, Lorenzo
dc.contributor.committeeMemberShakkottai, Sanjay
dc.creatorMurphy, James Thomas, III
dc.creator.orcid0000-0002-5530-8446
dc.date.accessioned2019-09-11T15:15:49Z
dc.date.available2019-09-11T15:15:49Z
dc.date.created2019-05
dc.date.issued2019-05
dc.date.submittedMay 2019
dc.date.updated2019-09-11T15:15:49Z
dc.description.abstractThis dissertation studies three applications of the tools of coupling and unimodularity in stationary settings. The first application is to exact coupling of random walks. Conditions for admitting a successful exact coupling are given that are necessary and in the Abelian case also sufficient. This solves a problem posed by H. Thorisson. The second application is centered on the random graph generated by a Doeblin-type coupling of discrete time processes whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a bridge graph, generated by paths started in a fixed state. The bridge graph is then made into a unimodular network. The final application focuses on point-shifts of point processes on topological groups. Foliations and connected components generated by point-shifts are studied, and the cardinality classification of connected components is generalized to unimodular groups.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/75807
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/2909
dc.language.isoen
dc.subjectExact coupling
dc.subjectRandom walk
dc.subjectDoeblin tree
dc.subjectEternal family tree
dc.subjectUnimodular network
dc.subjectMass-transport
dc.subjectPoint-shift
dc.subjectPoint process
dc.titleCoupling and unimodularity in stationary settings
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

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