8 papers
Finding all cospectral mates over a number field
Alexander Van Werde
We investigate a notion of cospectrality for integer matrices that is parameterized by algebraic number fields. Given a number field and a symmetric integer matrix, we wonder when…
Spectral graph clustering with inhomogeneous latent geometry
Konstantin Avrachenkov, Lucas S. Sibemberg, Alexander Van Werde
We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities.…
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…
Are sparse graphs typically determined by their spectrum?
Nils Van de Berg, Alexander Van Werde
We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of…
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…
Worst-case mixing estimates for Brownian motion with semipermeable barriers
Alexander Van Werde, Jaron Sanders
We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar dom…
A sufficient condition for generalized spectral characterization of graphs with loops
Alexander Van Werde
Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note e…
Recovering semipermeable barriers from reflected Brownian motion
Alexander Van Werde, Jaron Sanders
We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the bar…