Calculation of mean spectral density for statistically uniform treelike random models.
For random matrices with treelike structure there exists a recursive relation for the local Green functions whose solution permits us to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this article is to investigate and compare expressions for the spectral density of random regular graphs, based on easy approximations for real solutions of the recursive relation valid for trees with large coordination number. The obtained formulas are in a good agreement with the results of numerical calculations even for small coordination number.
Université Paris-Sud, CNRS, LPTMS, UMR8626, F-91405, Orsay, France.
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Bogomolny
Université Paris-Sud, CNRS, LPTMS, UMR8626, F-91405, Orsay, France.
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Giraud