• Upper Packing Dimension of a Measure and the Limit Distribution of Products of i.i.d. Stochastic Matrices

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/119/05/0669-0677

• Keywords

Packing dimension; stochastic matrices; Erdös sum; products of random matrices; continuous singularity of the limit distribution.

• Abstract

This article gives sufficient conditions for the limit distribution of products of i.i.d. $2\times 2$ stochastic matrices to be continuous singular, when the support of the distribution of the individual random matrices is countably infinite. It extends a previous result for which the support of the random matrices is finite. The result is based on adapting existing proofs in the context of attractors and iterated function systems to the case of infinite iterated function systems.

• Author Affiliations

1. Department of Mathematics, The University of Texas – Pan American, 1201 West University Drive, Edinburg, TX 78539, USA
2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
3. Departamento de Matemáticas, Universidad de Antioquia, Calle 67 N◦53-108, Medellín, Colombia, USA

• Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019