TY - JOUR

T1 - Asymptotics of a Fredholm Determinant Corresponding to the First Bulk Critical Universality Class in Random Matrix Models

AU - Bothner, Thomas

AU - Its, Alexander

PY - 2014/3/11

Y1 - 2014/3/11

N2 - We study the determinant det(I − KPII) of an integrable Fredholm operator KPII acting on the interval (−s,s) whose kernel is constructed out of the ﰪ-function associated with the Hastings–McLeod solution of the second Painlevé equation. This Fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random Hermitian matrix chosen from the unitary ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density. Using the Riemann–Hilbert method, we evaluate the large s-asymptotics of det(I − KPII).

AB - We study the determinant det(I − KPII) of an integrable Fredholm operator KPII acting on the interval (−s,s) whose kernel is constructed out of the ﰪ-function associated with the Hastings–McLeod solution of the second Painlevé equation. This Fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random Hermitian matrix chosen from the unitary ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density. Using the Riemann–Hilbert method, we evaluate the large s-asymptotics of det(I − KPII).

UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000335156700006&KeyUID=WOS:000335156700006

U2 - 10.1007/s00220-014-1950-z

DO - 10.1007/s00220-014-1950-z

M3 - Article (Academic Journal)

SP - 155

EP - 202

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -