Smallest singular value distribution and large gap asymptotics for products of random matrices

Manuela Girotti

We study the distribution of the smallest singular eigenvalues for the finite product of certain random matrix ensemble, in the limit where the size of the matrices becomes large. The limiting distributions that we will study can be expressed as Fredholm determinants of certain integral operators, and generalize in a natural way the extensively studied hard edge Bessel kernel determinant. We will express such quantities in terms of a 2x2 Riemann-Hilbert problem, and use this representation to obtain so-called large gap asymptotics

http://scgp.stonybrook.edu/video_portal/video.php?id=2503

Simons- Workshop: Six-vertex models, dimers, shapes, and all that