Title: Universality in unitary random matrix ensembles when the soft edge meets the hard edge Authors: Claeys, TomKuijlaars, Arno # Issue Date: 2008 Publisher: American Mathematical Society Host Document: Contemporary mathematics vol:458 pages:265-279 Conference: Conference on integrable systems, random matrices, and applications location:New York date:22-26 May 2006 Abstract: Unitary random matrix ensembles $Z^{-1}_{n,N} (det M)^\alpha exp(-N TrV(M))dM$ defined on positive definite matrices M, where $\alpha > -1$ and $V$ is real analytic, have a hard edge at $0$. The equilibrium measure associated with $V$ typically vanishes like a square root of soft edges of the spectrum. For the case that the equilibrium measure vanishes like a square root at $0$, we determine the scaling limits of the eigenvalue correlation kernel near $0$ in the limit when $n,N \rightarrow \infty$ such that $n/N - 1 = {cal O}(n^{-2/3})$. For each value of $\alpha > -1$ we find a one-parameter family of limiting kernels that we describe in terms of the Hastings-McLeod solution of the Painlevé II equation with parameter $\alpha + 1/2$. ISBN: 978-0-8218-4240-9 Publication status: published KU Leuven publication type: IC Appears in Collections: Analysis Section