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math-ph2023
Nodal decompositions of a symmetric matrix
Theo McKenzie, John Urschel
Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary sign…
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…