Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System
Related Research Unit(s)
|Journal / Publication||Communications in Mathematical Physics|
|Online published||8 Sep 2018|
|Publication status||Published - Jan 2019|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-85053451192&origin=recordpage|
We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of eigenvalues. We obtain Tracy–Widom formulas for the Fredholm determinants, which are explicitly given in terms of integrals involving a family of distinguished solutions to the coupled Painlevé II system in dimension four. Moreover, the large gap asymptotics for these Fredholm determinants are derived, where the constant terms are given explicitly in terms of the Riemann zeta-function.
Communications in Mathematical Physics, Vol. 365, No. 2, 01.2019, p. 515-567.
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal
Xu, S-X & Dai, D 2019, 'Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System', Communications in Mathematical Physics, vol. 365, no. 2, pp. 515-567. https://doi.org/10.1007/s00220-018-3257-y