游程编码序列的Rényi熵和模式匹配
Rényi entropy and pattern matching for run-length encoded sequences
摘要：
本文研究了游程编码序列的最长公共子串长度的渐近性质。当原始序列是由具有指数衰减的$α$ -混合过程（或具有多项式衰减的$ψ$ -混合过程）生成时，我们证明了该长度随依赖于前推测度的Rényi熵的系数而几何地增长。对于Bernoulli过程和马尔可夫链，这个系数是显式计算的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
