216 citations · 1.1k across the 36 of their papers we have counts for
37 papers
Preservation of algebraicity in free probability
Greg W. Anderson
We show that any matrix-polynomial combination of free noncommutative random variables each having an algebraic law has again an algebraic law. Our result answers a question raised…
Tridiagonalized GUE matrices are a matrix model for labeled mobiles
Abdelmalek Abdesselam, Greg W. Anderson, Alexander R. Miller
It is well-known that the number of planar maps with prescribed vertex degree distribution and suitable labeling can be represented as the leading coefficient of the -…
A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices
Greg W. Anderson
Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach…
Asymptotically liberating sequences of random unitary matrices
Greg W. Anderson, Brendan Farrell
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary ma…
Counting colored planar maps free-probabilistically
Abdelmalek Abdesselam, Greg W. Anderson
Our main result is an explicit operator-theoretic formula for the number of colored planar maps with a fixed set of stars each of which has a fixed set of half-edges with fixed col…
Convergence of the largest singular value of a polynomial in independent Wigner matrices
Greg W. Anderson
For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variabl…