R\'enyi entropy and pattern matching for run-length encoded sequences
Probability
2020-12-14 v2 Information Theory
Dynamical Systems
math.IT
Abstract
In this note, we studied the asymptotic behaviour of the length of the longest common substring for run-length encoded sequences. When the original sequences are generated by an -mixing process with exponential decay (or -mixing with polynomial decay), we proved that this length grows logarithmically with a coefficient depending on the R\'enyi entropy of the pushforward measure. For Bernoulli processes and Markov chains, this coefficient is computed explicitly.
Cite
@article{arxiv.2003.05500,
title = {R\'enyi entropy and pattern matching for run-length encoded sequences},
author = {Jerome Rousseau},
journal= {arXiv preprint arXiv:2003.05500},
year = {2020}
}