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math.PR2026
An Alon-Boppana Bound for the Non-Backtracking Operator
Theo McKenzie
For any fixed , we prove a lower bound on the th largest modulus of an eigenvalue of the non-backtracking matrix . Specifically, consider any deterministic or random famil…
math.PR2026
The Gaussian Wave for Graphs of Finite Cone Type
Amir Dembo, Theo McKenzie
We show that for any infinite tree of finite cone type satisfying a mild expansion condition, the only typical process on its vertices with covariance induced by the Green's functi…