Many Nodal Domains in Random Regular Graphs

Shirshendu Ganguly,Theo McKenzie,Sidhanth Mohanty,Nikhil Srivastava

arxiv（2023）

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摘要

Let G be a random d -regular graph on n vertices. 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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关键词

many nodal domains,random

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