NDLI: Random mappings of scaled graphs

Content Provider	Springer Nature Link
Author	Erschler, Anna
Copyright Year	2008
Abstract	Given a connected finite graph Γ with a fixed base point O and some graph G with a based point we study random 1-Lipschitz maps of a scaled Γ into G. We are mostly interested in the case where G is a Cayley graph of some finitely generated group, where the construction does not depend on the choice of base points. A particular case of Γ being a graph on two vertices and one edge corresponds to the random walk on G, and the case where Γ is a graph on two vertices and two edges joining them corresponds to Brownian bridge in G. We show, that unlike in the case $${G=\mathbb Z^d}$$ , the asymptotic behavior of a random scaled mapping of Γ into G may differ significantly from the asymptotic behavior of random walks or random loops in G. In particular, we show that this occurs when G is a free non-Abelian group. Also we consider the case when G is a wreath product of $${\mathbb Z}$$ with a finite group. To treat this case we prove new estimates for transition probabilities in such wreath products. For any group G generated by a finite set S we define a functor E from category of finite connected graphs to the category of equivalence relations on such graphs. Given a finite connected graph Γ, the value E G,S (Γ) can be viewed as an asymptotic invariant of G.
Ending Page	579
Page Count	37
Starting Page	543
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	144
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-05-08
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lamplighter groups Brownian bridges Random graph homomorphism Mathematical and Computational Physics Probability measures on groups or semigroups, Fourier transforms, factorization Probability Theory and Stochastic Processes Quantitative Finance Free groups Statistics for Business/Economics/Mathematical Finance/Insurance Probabilistic methods in group theory Operations Research/Decision Theory Geometric group theory Mathematical Biology in General Asymptotic properties of groups Lipschitz maps Random walks on groups
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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