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arXiv · 2003.05500

R\'enyi entropy and pattern matching for run-length encoded sequences

Jerome Rousseau
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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 $\alpha$-mixing process with exponential decay (or $\psi$-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.

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Jerome Rousseau. 2020-03-11. R\'enyi entropy and pattern matching for run-length encoded sequences. https://arxiv.org/abs/2003.05500

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