Periodic Walks on Large Regular Graphs and Random Matrix Theory

DOI10.1080/10586458.2014.950874zbMath1359.11078arXiv1105.4742OpenAlexW2100021431MaRDI QIDQ5498937

Uzy Smilansky, Idan Oren

Publication date: 11 February 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4742

zbMATH Keywords

regular graphsspectral statisticsadjacency eigenvaluesperiodic walks

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Relations with random matrices (11M50)

Cites Work

• The expected eigenvalue distribution of a large regular graph
• Automorphic forms and geometry of arithmetic varieties
• On orthogonal and symplectic matrix ensembles
• Discrete path integral approach to the Selberg trace formula for regular graphs
• Expander graphs and their applications
• A proof of Alon’s second eigenvalue conjecture and related problems
• Trace formulas and spectral statistics for discrete Laplacians on regular graphs (II)
• Trace formulae and spectral statistics for discrete Laplacians on regular graphs (I)
• Semiclassical theory of spectral rigidity
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• Random matrix theory and \(\zeta(1/2+it)\).

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