Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Operators associated with soft and hard spectral edges from unitary ensembles.
AU - Blower, Gordon
N1 - The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 337 (1), 2008, © ELSEVIER.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble.
AB - Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble.
KW - Random matrics
KW - GUE
KW - Hankel operators
KW - Sonine spaces
KW - Hill's equation
U2 - 10.1016/j.jmaa.2007.03.084
DO - 10.1016/j.jmaa.2007.03.084
M3 - Journal article
VL - 337
SP - 239
EP - 265
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -