On the eigenvalues of Erdos-Renyi random bipartite graphs

2021/03/14 by Calum J. Ashcroft, Ashcroft, Calum J.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2103.07918

openalex publication_date 2021/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyse the eigenvalues of Erdös--Rényi random bipartite graphs. In particular, we consider p satisfying n₁p=Ω(√n₁plog³(n₁)), n₂p=Ω(√n₂plog³(n₂)), and let G∼ G(n₁,n₂,p). We show that with probability tending to 1 as n₁ tends to infinity: μ₂ (A(G))≤ 2[1+o(1)](√n₁p+√n₂p+√(n₁+n₂)p).

Citations

• Spectra of Hypergraphs and Applications

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