English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider finite state, discrete-time, mixing Markov chains $(V,P)$, where$V$ is the state space and $P$ is transition matrix. To each such chain$(V,P)$, we associate a sequence of chains $(V_n,P_n)$ by coding trajectoriesof $(V,P)$ according to their overlapping $n$-blocks. The chain $(V_n,P_n)$,called the $n$-block Markov chain associated to $(V,P)$, may be considered analternate version of $(V,P)$ having memory of length $n$. Along such a sequenceof chains, we characterize the asymptotic behavior of coalescence times andmeeting times as $n$ tends to infinity. In particular, we define an algebraicquantity $L(V,P)$ depending only on $(V,P)$, and we show that if thecoalescence time on $(V_n,P_n)$ is denoted by $C_n$, then the quantity$\frac{1}{n} \log C_n$ converges in probability to $L(V,P)$ with exponentialrate. Furthermore, we fully characterize the relationship between $L(V,P)$ andthe entropy of $(V,P)$.

Coalescence and meeting times on $n$-block Markov chains