2 citations · 3 across the 5 of their papers we have counts for
7 papers
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…
Explicit two-sided unique-neighbor expanders
Jun-Ting Hsieh, Theo McKenzie, Sidhanth Mohanty +1
We study the problem of constructing explicit sparse graphs that exhibit strong vertex expansion. Our main result is the first two-sided construction of imbalanced unique-neighbor…
Many nodal domains in random regular graphs
Shirshendu Ganguly, Theo McKenzie, Sidhanth Mohanty +1
Let be a random -regular graph. We prove that for every constant , with high probability every eigenvector of the adjacency matrix of with eigenvalue less than $-2…
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…
High-girth near-Ramanujan graphs with lossy vertex expansion
Theo McKenzie, Sidhanth Mohanty
Kahale proved that linear sized sets in -regular Ramanujan graphs have vertex expansion and complemented this with construction of near-Ramanujan graphs with v…
Support of Closed Walks and Second Eigenvalue Multiplicity of the Normalized Adjacency Matrix
Theo McKenzie, Peter M. R. Rasmussen, Nikhil Srivastava
We show that the multiplicity of the second normalized adjacency matrix eigenvalue of any connected graph of maximum degree is bounded by for an…
A New Algorithm for the Robust Semi-random Independent Set Problem
Theo McKenzie, Hermish Mehta, Luca Trevisan
In this paper, we study a general semi-random version of the planted independent set problem in a model initially proposed by Feige and Kilian, which has a large proportion of adve…