1 citations · 1 across the 1 of their papers we have counts for
6 papers
Existence of the free energy for heavy-tailed spin glasses
Aukosh Jagannath, Patrick Lopatto
We study the free energy of a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean,…
Eigenvector Statistics of Lévy Matrices
Amol Aggarwal, Patrick Lopatto, Jake Marcinek
We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called Lévy matrices) whose associated eigenvalues are sufficiently small. We show tha…
Universality of the least singular value for the sum of random matrices
Ziliang Che, Patrick Lopatto
We consider the least singular value of , where are independent Haar-distributed unitary matrices and are deterministic diagonal matrices. Un…
Tail bounds for gaps between eigenvalues of sparse random matrices
Patrick Lopatto, Kyle Luh
We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and er…
Comparison theorem for some extremal eigenvalue statistics
Benjamin Landon, Patrick Lopatto, Jake Marcinek
We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of…
GOE Statistics for Levy Matrices
Amol Aggarwal, Patrick Lopatto, Horng-Tzer Yau
In this paper we establish eigenvector delocalization and bulk universality for Lévy matrices, which are real, symmetric, random matrices whose upper tria…