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The limit theorem with respect to the matrices on non-backtracking paths of a graph

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 Added by Shingo Sugiyama
 Publication date 2020
  fields
and research's language is English




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We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak.



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