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 study the distribution of the number of (non-backtracking) periodic walkson large regular graphs. We propose a formula for the ratio between thevariance of the number of $t$-periodic walks and its mean, when the cardinalityof the vertex set $V$ and the period $t$ approach $\infty$ with $t/V\rightarrow\tau$ for any $\tau$. This formula is based on the conjecture that the spectralstatistics of the adjacency eigenvalues is given by Random Matrix Theory (RMT).We provide numerical and theoretical evidence for the validity of thisconjecture. The key tool used in this study is a trace formula which expressesthe spectral density of $d$-regular graphs, in terms of periodic walks.

Periodic Walks on Large Regular Graphs and Random Matrix Theory