On the Largest Eigenvalue of a Random Subgraph of the Hypercube

Details On the Largest Eigenvalue of a Random Subgraph of the Hypercube On the Largest Eigenvalue of a Random Subgraph of the Hypercube

2002-09-14

arxiv.org/abs/math/0209178v2

Mathematics

Probability

Final version (to appear in Commun. Math. Phys.)

Scientific paper

10.1007/s00220-003-0872-y

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 \lambda_1(G)= (1+o(1))
max(\Delta^{1/2}(G),np), where \Delta(G) is the maximum degree of G and o(1)
term tends to zero as max (\Delta^{1/2}(G), np) tends to infinity.

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