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Random Walks on Graphs and Approximation of L2-Invariants

icon-email Andrew Kricker , Zenas Wong

Abstract

In this work, we interpret right multiplication operators Rw:l2(G)→l2(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.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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