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math.PR2026
On the satisfaction frequency of spectral characterization conditions
Nikita Lvov, Alexander Van Werde
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from…
math.PR2026
Exact cospectrality probabilities for uniform random matrices
Alexander Van Werde
We study the conjugation action of orthogonal matrices on symmetric random matrices. Given a fixed orthogonal matrix over an algebraic number field and a random matrix with entries…