We consider the adjacency matrix A of a large random graph and study fluctuations of the function f(n)(z, u) = (1/n)Sigma(n)(k=1)exp{-uG(kk)(z)} with G(z) = (z-iA)(-1). We prove that the moments of fluctuations normalized by n(-1/2) in the limit n ->infinity satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for Tr G(z) and then extend the result on the linear eigenvalue statistics Tr phi(A) of any function phi:R -> R which increases, together with its first two derivatives, at infinity not faster than an exponential. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3299297]
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs / Tirozzi, Benedetto; Masha, Shcherbina. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 51:2(2010), pp. 023523-1-023523-20. [10.1063/1.3299297]
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
TIROZZI, Benedetto;
2010
Abstract
We consider the adjacency matrix A of a large random graph and study fluctuations of the function f(n)(z, u) = (1/n)Sigma(n)(k=1)exp{-uG(kk)(z)} with G(z) = (z-iA)(-1). We prove that the moments of fluctuations normalized by n(-1/2) in the limit n ->infinity satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for Tr G(z) and then extend the result on the linear eigenvalue statistics Tr phi(A) of any function phi:R -> R which increases, together with its first two derivatives, at infinity not faster than an exponential. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3299297]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
