On asymptotic solvability of random graph's laplacians

Details On asymptotic solvability of random graph's laplacians On asymptotic solvability of random graph's laplacians

2000-09-19

arxiv.org/abs/math-ph/0009028v1

Physics

Mathematical Physics

LaTeX, 6 pages

Scientific paper

We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency matrix of G. These relations allow one to study the corresponding eigenvalue distribution function; we show that its density has an infinite support in contrast to the case of the ordinary discrete Laplacian.

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