Nathan Albin, Joan Lind, Anna Melikyan, Pietro Poggi-Corradini
Published 2024-04-09Version 1
In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be bounded away from zero and for the existence of a minimizing set of weights. These conditions are given both in terms of properties of random spanning trees and in terms of a type of density on graphs. These results generalize and extend the work of [7].
On random $\pm 1$ matrices: Singularity and Determinant
Condensation of Determinants
On the determinant of hexagonal grids $H_{k,n}$
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