TY - JOUR
T1 - Mixed moments of characteristic polynomials of random unitary matrices
AU - Bailey, E. C.
AU - Bettin, S.
AU - Blower, G.
AU - Conrey, J. B.
AU - Prokhorov, A.
AU - Rubinstein, M. O.
AU - Snaith, N. C.
PY - 2019/8/23
Y1 - 2019/8/23
N2 - Following the work of Conrey, Rubinstein, and Snaith [Commun. Math. Phys. 267, 611 (2006)] and Forrester and Witte [J. Phys. A: Math. Gen. 39, 8983 (2006)], we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a PainlevĂ© differential equation. We also calculate a simple form for the asymptotic behavior of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.
AB - Following the work of Conrey, Rubinstein, and Snaith [Commun. Math. Phys. 267, 611 (2006)] and Forrester and Witte [J. Phys. A: Math. Gen. 39, 8983 (2006)], we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a PainlevĂ© differential equation. We also calculate a simple form for the asymptotic behavior of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.
UR - http://www.scopus.com/inward/record.url?scp=85071580273&partnerID=8YFLogxK
U2 - 10.1063/1.5092780
DO - 10.1063/1.5092780
M3 - Article (Academic Journal)
AN - SCOPUS:85071580273
VL - 60
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 8
M1 - 083509
ER -