Local Law for Eigenvalues of Random Regular Bipartite Graphs
- 16 Downloads
In this paper, we study the local law for eigenvalues of large random regular bipartite graphs with degree growing moderately fast. We prove that the empirical spectral distribution of the adjacency matrix converges in probability to a scaled down copy of the Marchenko–Pastur distribution on intervals of short length.
KeywordsRandom bipartite regular graphs Marchenko–Pastur law Wishart matrix
Mathematics Subject Classification05C80 60G57
The author thanks I. Dumitriu for bringing the problem to his attention. Part of this work was done while the author was at the Mathematics Department, University of Washington. The author also thanks the anonymous referee who provided many useful suggestions.
- 5.Friedman, J.: A proof of Alon’s second eigenvalue conjecture. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 720–724. ACM (2003)Google Scholar