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pro vyhledávání: '"Anderson, Greg W."'
Autor:
Anderson, Greg W.
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 by a recent paper of Shlyakhtenko and Skoufranis. The result belongs
Externí odkaz:
http://arxiv.org/abs/1406.6664
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 $\frac{1}{N}$-expansion of a joint cumulant of traces of powers of an $N$-by-$N$ GUE
Externí odkaz:
http://arxiv.org/abs/1404.7415
Autor:
Anderson, Greg W.
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 is to adapt some techniques from one of the recent papers of Erd\"os-
Externí odkaz:
http://arxiv.org/abs/1308.4668
Autor:
Anderson, Greg W., Farrell, Brendan
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 matrices delivers asymptotic freeness. In this paper we exhibit many oth
Externí odkaz:
http://arxiv.org/abs/1302.5688
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 coloration. The formula bounds the number of such colored planar maps wel
Externí odkaz:
http://arxiv.org/abs/1203.3185
Autor:
Anderson, Greg W.
Publikováno v:
Annals of Probability 2013, Vol. 41, No. 3B, 2103-2181
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 variables, under fourth moment hypotheses. We actually prove a more general r
Externí odkaz:
http://arxiv.org/abs/1103.4825
Autor:
Anderson, Greg W, Thakur, Dinesh S
We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially involved relation
Externí odkaz:
http://arxiv.org/abs/0902.1180
Autor:
Anderson, Greg W., Zeitouni, Ofer
Publikováno v:
Annals of Statistics 2008, Vol. 36, No. 6, 2553-2576
We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to t
Externí odkaz:
http://arxiv.org/abs/math/0612791