On asymptotic solvability of random graph's laplacians

2000/09/19 by A. Khorunzhy, Khorunzhy, A., V. Vengerovsky +2 · 2 citations
Mathematics · Physics and Astronomy · #05C80 (Primary) #15A52 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #math-ph #math.MP #msc:05C80 #msc:15A52

paper · pdf · doi:10.48550/arxiv.math-ph/0009028

LaTeX, 6 pages

arxiv created 2000/09/19 · openalex publication_date 2000/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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