Some Questions in Painleve Equations and Random Matrix Theory Painleve
DescriptionIn this project, we will further investigate the applications of Painleve equations in random matrix theory. We will consider new critical cases, study the corresponding eigenvalue distribution, and derive new limiting eigenvalue correlation kernels. In certain situations, we expect new limiting kernels will be given in terms of functions related to the Painleve equations or their higher order generalizations. Then, we will study gap probabilities (the probability that there is no eigenvalue in certain intervals) by considering Fredholm determinants of the limiting correlation kernels. We will derive close-form representations of the Fredholm determinants explicitly, as well as their asymptotics when the gap is large.
|Effective start/end date||1/09/19 → …|