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math-ph2025
Nodal Count for Orthogonally Invariant Ensembles
Lior Alon, Dan Mikulincer, John Urschel
We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particu…
math.CO2025
On the Maximum Spread of Non-Negative Matrices
Susie Lu, John Urschel
Given a directed graph , the spread of is the largest distance between any two eigenvalues of its adjacency matrix. In 2022, Breen, Riasanovsky, Tait, and Urschel asked what…
math.OC2025
A Class of Optimal Directed Graphs for Network Synchronization
Susie Lu, John Urschel, Ji Liu
In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Throu…