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arXiv · 2109.11532

Many nodal domains in random regular graphs

Shirshendu Ganguly·Theo McKenzie·Sidhanth Mohanty·Nikhil Srivastava
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Abstract

Let $G$ be a random $d$-regular graph. We prove that for every constant $\alpha > 0$, with high probability every eigenvector of the adjacency matrix of $G$ with eigenvalue less than $-2\sqrt{d-2}-\alpha$ has $\Omega(n/$polylog$(n))$ nodal domains.

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Shirshendu Ganguly, Theo McKenzie, Sidhanth Mohanty, Nikhil Srivastava. 2021-09-23. Many nodal domains in random regular graphs. https://doi.org/10.1007/s00220-023-04709-6

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