This article is available for purchase or by subscription. See below.
Abstract
|
A family of random variables
,
depending on a real parameter
,
appears in the asymptotics of the joint moments of characteristic polynomials of
random unitary matrices and their derivatives (Assiotis et al. 2020), in the ergodic
decomposition of the Hua–Pickrell measures (Borodin and Olshanski 2001 and Qiu
2017), and conjecturally in the asymptotics of the joint moments of Hardy’s
function and its derivative (Hughes 2001 and Assiotis et al. 2020). Our first
main result establishes a connection between the characteristic function of
and the
-Painlevé
equation in the full range
of parameter values
.
Our second main result gives the first explicit expression for the
density and all the complex moments of the absolute value of
for integer
values of
.
Finally, we establish an analogous connection to another special case of the
-Painlevé
equation for the Laplace transform of the sum of the inverse points of the Bessel
point process.
|
PDF Access Denied
We have not been able to recognize your IP address
34.234.83.135
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
characteristic polynomials, random unitary matrices,
Painlevé equations, joint moments, Hardy's function
|
Mathematical Subject Classification
Primary: 11M50, 15B52, 33E17, 60B20
|
Milestones
Received: 14 September 2020
Revised: 9 January 2021
Accepted: 23 February 2021
Published: 15 October 2021
|
|