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On weak limits and unimodular measures.

Artemenko, Igor.

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On weak limits and unimodular measures.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	On weak limits and unimodular measures./
作者:	Artemenko, Igor.
面頁冊數:	0 p.
附註:	Source: Masters Abstracts International, Volume: 52-06.
Contained By:	Masters Abstracts International52-06(E).
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=MS26694
ISBN:	9780499266941

On weak limits and unimodular measures.
Artemenko, Igor.

On weak limits and unimodular measures. - 0 p.

Source: Masters Abstracts International, Volume: 52-06.

Thesis (M.Sc.)--University of Ottawa (Canada), 2014.

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.

ISBN: 9780499266941Subjects--Topical Terms:

1669109
Applied Mathematics.

On weak limits and unimodular measures.
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245 1 0 $a On weak limits and unimodular measures.
300 $a 0 p.
500 $a Source: Masters Abstracts International, Volume: 52-06.
502 $a Thesis (M.Sc.)--University of Ottawa (Canada), 2014.
520 $a 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.
590 $a School code: 0918.
650 4 $a Applied Mathematics. $3 1669109
690 $a 0364
710 2 $a University of Ottawa (Canada). $b Mathematiques et statistique / Mathematics and Statistics. $3 2101115
773 0 $t Masters Abstracts International $g 52-06(E).
790 $a 0918
791 $a M.Sc.
792 $a 2014
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=MS26694