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

The involution walk is the random walk on $S_n$ generated by involutions witha binomially distributed with parameter $1-p$ number of $2$-cycles. This is aparallelization of the transposition walk. The involution walk is shown in thispaper to mix for $\frac{1}{2} \leq p \leq 1$ fixed, $n$ sufficiently large inbetween $\log_{1/p}(n)$ steps and $\log_{2/(1+p)}(n)$ steps. The paperintroduces a new technique for finding eigenvalues of random walks on thesymmetric group generated by many conjugacy classes using the characterpolynomial for the characters of the representations of the symmetric group.Monotonicity relations used in the bound also give after sufficient time thelikelihood order, the asymptotic order from most likely to least likelypermutation. The walk was introduced to study a conjecture about a random walkon the unitary group from the information theory of black holes.

A random walk on the symmetric group generated by random involutions