12 papers
Comparison theorems for the extreme eigenvalues of a random symmetric matrix
Joel A. Tropp
This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matr…
Linear algebra at exponential scale via tensor network dimension reduction
Chris Camaño, Ethan N. Epperly, Raphael A. Meyer +1
Many problems in modern scientific computing are challenging because of a \emph{curse of dimension}, where their mathematical formulation involves objects whose dimension is \emph{…
Applied Random Matrix Theory
Joel A. Tropp
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerfu…
Concentration for random product formulas
Chi-Fang Chen, Hsin-Yuan Huang, Richard Kueng +1
Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulati…
Universality laws for random matrices via exchangeable counterparts
Joel A. Tropp
Recently, Brailovskaya & van Handel (GAFA, 2024) established a suite of nonasymptotic universality laws which demonstrate that the spectral statistics of an independent sum of rand…
Successive randomized compression: A randomized algorithm for the compressed MPO-MPS product
Chris Camaño, Ethan N. Epperly, Joel A. Tropp
Tensor networks like matrix product states (MPSs) and matrix product operators (MPOs) are powerful tools for representing exponentially large states and operators, with application…