D Dong, T McKenzie - arXiv preprint arXiv:2412.09570, 2024 - arxiv.org
We prove that for each $ d\geq 3$ and $ k\geq 2$, the set of limit points of the first $ k $ eigenvalues of sequences of $ d $-regular graphs is\[\{(\mu_1,\dots,\mu_k) …
Y Chen - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
Abstract A (d 1 d 2)-biregular bipartite graph G=(L∪ R, E) is called left-(m, δ) unique- neighbor expander iff each subset S of the left vertices with| S|≤ m has at least δd 1| S …
A Kamber, T Kaufman - Proceedings of the 54th Annual ACM SIGACT …, 2022 - dl.acm.org
The question of finding expander graphs with strong vertex expansion properties such as unique neighbor expansion and lossless expansion is central to computer science. A barrier …
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete Poincar\'e inequality for scalar functions, also …
Y Chen - arXiv preprint arXiv:2410.07061, 2024 - arxiv.org
A $(d_1, d_2) $-biregular bipartite graph $ G=(L\cup R, E) $ is called left-$(m,\delta) $ unique-neighbor expander iff each subset $ S $ of the left vertices with $| S|\leq m $ has at …
A popular way of analyzing a graph is through spectral properties of its associated matrices, such as the adjacency matrix or the Laplacian matrix. This type of analysis has produced …
Discrete graphs are ubiquitous models applicable to many areas, useful for any discrete system with some notion of connectivity. Some examples for which these are useful are …
T McKenzie - Comptes Rendus. Mathématique, 2022 - numdam.org
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 …
MASTERARBEIT / MASTER’S THESIS Page 1 MASTERARBEIT / MASTER’S THESIS Titel der Masterarbeit / Title of the Master’s Thesis Margulis’ Expanders and Ramanujan Graphs …