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math.PR2021
Many nodal domains in random regular graphs
Shirshendu Ganguly, Theo McKenzie, Sidhanth Mohanty +1
Let be a random -regular graph. We prove that for every constant , with high probability every eigenvector of the adjacency matrix of with eigenvalue less than $-2…
math-ph2021
The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph
Theo McKenzie
Anantharaman and Le Masson proved that any family of eigenbases of the adjacency operators of a family of graphs is quantum ergodic (a form of delocalization) assuming the graphs s…