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Title: Random walks on graphs and approximation of L²-Invariants
Authors: Kricker, Andrew
Wong, Zenas
Keywords: Science::Mathematics
Issue Date: 2021
Source: Kricker, A. & Wong, Z. (2021). Random walks on graphs and approximation of L²-Invariants. Acta Mathematica Vietnamica, 46(2), 309-319.
Project: RG 32/17 
Journal: Acta Mathematica Vietnamica 
Abstract: In this work, we interpret right multiplication operators Rw: l2(G) → l2(G) , w∈ ℂ[G] as random walk operators on certain labelled graphs we employ that are analogous to Cayley graphs. Applying a generalization of the graph convergence defined by R. I. Grigorchuk and A. Żuk to these graphs gives a new interpretation and proof of a special case of W. Lück’s famous Theorem on the Approximation of L2-Betti numbers for countable residually finite groups by means of exhausting towers of finite-index subgroups. In particular, using this interpretation, the theorem follows naturally from standard theorems in probability theory concerning the weak convergence of probability measures that are characterized by their moments. This paper is mainly a direct adaptation of the ideas of Grigorchuk, Zuk̇ and Lück to this setting. We aim to explain how these ideas are related and give a short exposition of them.
ISSN: 0251-4184
DOI: 10.1007/s40306-021-00425-2
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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