The Tracy--Widom law for some sparse random matrices

Abstract

Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution.

The proof contains a serious mistake, and Lemma 5 can not be true as stated. For example, the probability that the graph is not connected tends to zero slower than eq. 4 would imply. I am grateful to Charles Bordenave and Sandrine Péché who brought this to my attention

References in corpus (2)

• Random matrices, non-backtracking walks, and orthogonal polynomials
• Even Walks and Estimates of High Moments of Large Wigner Random Matrices

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