We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer G-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a 2x2 Riemann-Hilbert problem, and use this representation to obtain the so-called large gap asymptotics. The paper is available on arxiv: https://arxiv.org/abs/1612.01916 Speaker(s): Manuela Girotti (Colorado State University)