title: Finite-size corrections to the spectrum of regular random graphs: An analytical solution.
abstract: We develop a thorough analytical study of the O(1/N) correction to the spectrum of regular random graphs with N→∞ nodes. The finite-size fluctuations of the resolvent are given in terms of a weighted series over the contributions coming from loops of all possible lengths, from which we obtain the isolated eigenvalue as well as an analytical expression for the O(1/N) correction to the continuous part of the spectrum. The comparison between this analytical formula and direct diagonalization results exhibits an excellent agreement, confirming the correctness of our expression.
authors.affiliation: Dip. Fisica, Università La Sapienza, Piazzale A. Moro 2, I-00185, Rome, Italy.
authors.forename: F L
authors.initials: FL
authors.lastname: Metz
authors.affiliation: Dip. Fisica, Università La Sapienza, Piazzale A. Moro 2, I-00185, Rome, Italy and IPCF-CNR, UOS Roma Kerberos, Università La Sapienza, Piazzale A. Moro 2, I-00185, Rome, Italy and INFN, Piazzale A. Moro 2, 00185, Rome, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Parisi
authors.affiliation: Dip. Fisica, Università La Sapienza, Piazzale A. Moro 2, I-00185, Rome, Italy and IPCF-CNR, UOS Roma Kerberos, Università La Sapienza, Piazzale A. Moro 2, I-00185, Rome, Italy.
authors.forename: L
authors.initials: L
authors.lastname: Leuzzi