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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…
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…
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…
Comparison theorems for the minimum eigenvalue of a random positive-semidefinite matrix
Joel A. Tropp
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum ei…
A new approach to strong convergence
Chi-Fang Chen, Jorge Garza-Vargas, Joel A. Tropp +1
A family of random matrices is said to converge strongly to a family of bounded operators when $\|P(\bolds…
Nonlinear Matrix Concentration via Semigroup Methods
De Huang, Joel A. Tropp
Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the operator norm. This paper use…