1. bookVolumen 15 (2020): Edición 2 (December 2020)
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2309-5377
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30 Dec 2013
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Word Metric, Stationary Measure and Minkowski’s Question Mark Function

Publicado en línea: 25 Dec 2020
Volumen & Edición: Volumen 15 (2020) - Edición 2 (December 2020)
Páginas: 23 - 38
Recibido: 20 Jun 2020
Aceptado: 14 Jul 2020
Detalles de la revista
License
Formato
Revista
eISSN
2309-5377
Primera edición
30 Dec 2013
Calendario de la edición
2 veces al año
Idiomas
Inglés
Abstract

Given a countably infinite group G acting on some space X, an increasing family of finite subsets Gn, xX and a function f over X we consider the sums Sn(f, x) = ∑g∈Gnf(gx). The asymptotic behaviour of Sn(f, x) is a delicate problem that was studied under various settings. In the following paper we study this problem when G is a specific lattice in SL (2, ℤ ) acting on the projective line and Gn are chosen using the word metric. The asymptotic distribution is calculated and shown to be tightly connected to Minkowski’s question mark function. We proceed to show that the limit distribution is stationary with respect to a random walk on G defined by a specific measure µ. We further prove a stronger result stating that the asymptotic distribution is the limit point for any probability measure over X pushed forward by the convolution power µ∗n.

Keywords

MSC 2010

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