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

Following the derivation of the trace formulae in the first paper in thisseries, we establish here a connection between the spectral statistics ofrandom regular graphs and the predictions of Random Matrix Theory (RMT). Thisfollows from the known Poisson distribution of cycle counts in regular graphs,in the limit that the cycle periods are kept constant and the number ofvertices increases indefinitely. The result is analogous to the so called"diagonal approximation" in Quantum Chaos. We also show that by assuming thatthe spectral correlations are given by RMT to all orders, we can compute theleading deviations from the Poisson distribution for cycle counts. We providenumerical evidence which supports this conjecture.

Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II)