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Self-similar random measures are locally scale invariant

✍ Scribed by N. Patzschke; M. Zähle

Publisher
Springer
Year
1993
Tongue
English
Weight
635 KB
Volume
97
Category
Article
ISSN
1432-2064

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📜 SIMILAR VOLUMES

Self-similar random measures
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✍ U. Zähle 📂 Article 📅 1988 🏛 Springer 🌐 English ⚖ 939 KB

A set is called self-similar if it is decomposable into parts which are similar to the whole. This notion was generalized to random sets. In the present paper an alternative, axiomatic approach is given which makes precise the following idea (using Palm distribution theory): A random set is statisti

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We shall show that the oscillations observed by R. S. Strichartz in the Fourier transforms of self-similar measures have a large-scale renormalisation given by a Riesz measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.

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✍ Ying Xiong; Zhi-Xiong Wen 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 124 KB

## Abstract In this paper we study the limit behavior of weighted averages of some random sequence related to Bernoulli random variables, and apply the results to average density of self‐similar measures. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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✍ L. Olsen 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 205 KB

Let K and µ be the self-similar set and the self-similar measure associated with an iterated function system with probabilities (Si, pi)i=1,...,N satisfying the Open Set Condition. Let Σ = {1, . . . , N} N denote the full shift space and let π : Σ → K denote the natural projection. The (symbolic) lo