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Asymptotic theory of path spaces of graded graphs and its applications

Content Provider	Springer Nature Link
Author	Vershik, Anatoly M.
Copyright Year	2016
Abstract	The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The main subject is the asymptotic structure of filtrations and a new notion of standardness. All graded graphs and all filtrations of Borel or measure spaces can be divided into two classes: the standard ones, which have a regular behavior at infinity, and the other ones. Depending on this property, the list of invariant measures can either be well parameterized or have no good parametrization at all. One of the main results is a general standardness criterion for filtrations. We consider some old and new examples which illustrate the usefulness of this point of view and the breadth of its applications.
Starting Page	151
Ending Page	218
Page Count	68
File Format	PDF
ISSN	02892316
Journal	Japanese Journal of Mathematics
Volume Number	11
Issue Number	2
e-ISSN	18613624
Language	English
Publisher	Springer Japan
Publisher Date	2016-06-29
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	graded graph Markov compactum cotransition probability central measure filtration standardness limit shape Relations with the theory of $C^*$-algebras Probability measures on topological spaces Asymptotic theory of convex bodies Mathematics History of Mathematical Sciences
Content Type	Text
Resource Type	Article
Subject	Mathematics

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