论文标题
rényi熵和模式匹配的跑步编码序列
Rényi entropy and pattern matching for run-length encoded sequences
论文作者
论文摘要
在本说明中，我们研究了运行长度编码序列的最长常见基因长度的渐近行为。当原始序列是由$α$混合过程产生的，并具有指数衰减（或$ψ$ - 混合多项式衰减）时，我们证明了此长度根据推送措施的Rényi熵而对数增长。对于Bernoulli过程和Markov链，该系数是明确计算的。
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.
