Random walks in the group of euclidean isometries and self-similar measures

Elon Lindenstrauss, Péter P. Varjú

Research output: Contribution to journalArticlepeer-review

Abstract

We study products of random isometries acting on Euclidean space. Building on previous work of the second author, we prove a local limit theorem for balls of shrinking radius with exponential speed under the assumption that a Markov operator associated to the rotation component of the isometries has spectral gap. We also prove that certain self-similar measures are absolutely continuous with smooth densities. These families of self-similar measures give higher-dimensional analogues of Bernoulli convolutions on which absolute continuity can be established for contraction ratios in an open set.

Original languageAmerican English
Pages (from-to)1061-1127
Number of pages67
JournalDuke Mathematical Journal
Volume165
Issue number6
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics

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