Rényi entropy and pattern matching for run-length encoded sequences

03/11/2020

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by   Jerome Rousseau, et al.

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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 α-mixing process with exponential decay (or ψ-mixing with polynomial decay), we proved that this length grows logarithmically with a coefficient depending on the Rényi entropy of the pushforward measure. For Bernoulli processes and Markov chains, this coefficient is computed explicitly.