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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove an upper bound on the total variation mixing time of a finite Markovchain in terms of the absolute spectral gap and the number of elements in thestate space. Unlike results requiring reversibility or irreducibility, thisbound is finite whenever the chain converges. The dependence on the number ofelements means that the new bound cannot capture the behavior of rapidly mixingchains; but an example shows that such dependence is necessary. We also providea sharpened result for reversible chains that are not necessarily irreducible.The proof of the general bound exploits a connection between linear recurrencerelations and Schur functions due to Hou and Mu, while the sharpened bound forreversible chains arises as a consequence of the stochastic interpretation ofeigenvalues developed by Diaconis, Fill, and Miclo. In particular, for everyreversible chain with nonnegative eigenvalues $\beta_j$ we find a strongstationary time whose law is the sum of independent geometric random variableshaving mean $1/(1-\beta_j)$.

General mixing time bounds for finite Markov chains via the absolute spectral gap