On the Largest Eigenvalue of a Random Subgraph of the Hypercube

Alexander Soshnikov, Benny Sudakov
2003 Communications in Mathematical Physics  
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ_1(G)= (1+o(1)) max(Δ^1/2(G),np), where Δ(G) is the maximum degree of G and o(1) term tends to zero as max (Δ^1/2(G), np) tends to infinity.
doi:10.1007/s00220-003-0872-y fatcat:bjc27sf3nvbwxbkkagzischqhu