We address a class of problems in Unitary Ensemble. Specifically, we study the probability tyhat a gap sysmetric about 0, i.e., $(-a,a)$ is found in the Gaussian Unitary ensembles (GUE) and the Jacobi Unitary ensembles (JUE) (where in the JUE, we take the parameters $\alpha=\beta$.) By exploiting the even parity of the weight, a doubling of the interval to $(a^2,\infty)$ for the GUE, and $(a^2,1)$ for the (symmetric) JUE, shows that the gap probabilities maybe determined as the product of the smallest eigenvalue distributions the LUE with parameter $\alpha=-1/2$ and$\alpha=1/2$ and the (shifted) JUE with weights x^{1/2} (1-x)^{\beta) and $x^{-1/2} (1-x)^{\beta}$.

Chen is a mathematical physicst, he was a faculty member of the mathemtics department of imperial college, from 1992 to 2012, rising through the ranks, as Lecturer, Reader and Professor (Personal Chair) of Mathematical Physics. Upon the suggestion of a Senior Mathematician at the Univeristy of Macau, Chen becomes Professor of Mathematics, in the Univeristy of Macau, in August 2012. Chen is the Editor In Chief of the Journal, Random Matrices: Theory and Applications, which has it first impact factor 1.351 (gained in 2016).