Many nodal domains in random regular graphs

09/23/2021
by   Shirshendu Ganguly, et al.
0

Let G be a random d-regular graph. We prove that for every constant α > 0, with high probability every eigenvector of the adjacency matrix of G with eigenvalue less than -2√(d-2)-α has Ω(n/polylog(n)) nodal domains.

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