The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

AGA

Seminar

Periodic walks on random graphs and random matrix theory

Smilansky, U (Weizmann Institute of Science)
Tuesday 27 July 2010, 09:00-10.00

Seminar Room 1, Newton Institute

Abstract

The spectral statistics of the discrete Laplacian of d-regular graphs on V vertices are intimately connected with the distribution of the number of cycles of period t (t-cycles) on the graph. I shall discuss this connection by using a trace formula which expresses the spectral density in terms of the t-cycle counts. The trace formula will be used to write the spectral pair correlations in terms of the properly normalized variance of the t-cycle counts. Based on these results, I would like to propose a conjecture which uses Random Matrix Theory to compute the variance of the t-periodic cycle counts in the limit V,t -> infinity fixed value of with t/V. Numerical computations support this conjecture.

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧