52 citations · 61 across the 7 of their papers we have counts for
8 papers
Overlaps, Eigenvalue Gaps, and Pseudospectrum under real Ginibre and Absolutely Continuous Perturbations
Jess Banks, Jorge Garza Vargas, Archit Kulkarni +1
Let be an matrix with real i.i.d. entries, let be a real matrix with , and let . We show that with p…
Spectra of infinite graphs via freeness with amalgamation
Jorge Garza-Vargas, Archit Kulkarni
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For op…
Gaussian Regularization of the Pseudospectrum and Davies' Conjecture
Jess Banks, Archit Kulkarni, Satyaki Mukherjee +1
A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every…
The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Output
Jorge Garza-Vargas, Archit Kulkarni
We study the Lanczos algorithm where the initial vector is sampled uniformly from . Let be an Hermitian matrix. We show that when run for few ite…
Sets Characterized by Missing Sums and Differences in Dilating Polytopes
Thao Do, Archit Kulkarni, Steven J. Miller +3
A sum-dominant set is a finite set of integers such that . As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to…
Sums and differences of correlated random sets
Thao Do, Archit Kulkarni, Steven J. Miller +2
Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum…