On Weak Limits and Unimodular Measures

In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle...

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Main Author: Artemenko, Igor
Language:en
Published: 2014
Subjects:
law
Online Access:http://hdl.handle.net/10393/30417
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OOU.#10393-304172014-06-14T03:50:34ZOn Weak Limits and Unimodular MeasuresArtemenko, IgortreeautomorphismgroupballpathconnectedcomponentrootedbirootedgraphCayleyconverges weaklyextreme pointmass transport principleinvolution invariancelawneighbourhoodorbitrigidsubgraphunimodularunimodularityvertex-transitivewalkweak limitweak convergenceprobabilitymeasurebarred binary treebi-infinite pathfirst ancestorjudiciallawlessnegligiblestabilizersustainedstrictly sustainedrandom graphIn this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.2014-01-14T22:03:20Z2014-01-14T22:03:20Z20142014-01-14Thèse / Thesishttp://hdl.handle.net/10393/30417en
collection NDLTD
language en
sources NDLTD
topic tree
automorphism
group
ball
path
connected
component
rooted
birooted
graph
Cayley
converges weakly
extreme point
mass transport principle
involution invariance
law
neighbourhood
orbit
rigid
subgraph
unimodular
unimodularity
vertex-transitive
walk
weak limit
weak convergence
probability
measure
barred binary tree
bi-infinite path
first ancestor
judicial
lawless
negligible
stabilizer
sustained
strictly sustained
random graph
spellingShingle tree
automorphism
group
ball
path
connected
component
rooted
birooted
graph
Cayley
converges weakly
extreme point
mass transport principle
involution invariance
law
neighbourhood
orbit
rigid
subgraph
unimodular
unimodularity
vertex-transitive
walk
weak limit
weak convergence
probability
measure
barred binary tree
bi-infinite path
first ancestor
judicial
lawless
negligible
stabilizer
sustained
strictly sustained
random graph
Artemenko, Igor
On Weak Limits and Unimodular Measures
description In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.
author Artemenko, Igor
author_facet Artemenko, Igor
author_sort Artemenko, Igor
title On Weak Limits and Unimodular Measures
title_short On Weak Limits and Unimodular Measures
title_full On Weak Limits and Unimodular Measures
title_fullStr On Weak Limits and Unimodular Measures
title_full_unstemmed On Weak Limits and Unimodular Measures
title_sort on weak limits and unimodular measures
publishDate 2014
url http://hdl.handle.net/10393/30417
work_keys_str_mv AT artemenkoigor onweaklimitsandunimodularmeasures
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