Corpus ID: 237605157

Many nodal domains in random regular graphs

@article{Ganguly2021ManyND,
  title={Many nodal domains in random regular graphs},
  author={Shirshendu Ganguly and Theo McKenzie and Sidhanth Mohanty and Nikhil Srivastava},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.11532}
}
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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