VARIANCE CALCULATIONS AND THE BESSEL KERNEL

In the Laguerre ensemble of N x N Hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted var(N)f, as N-->infinity. Furthermore, this statistic often contains an additional parameter alpha for which the limit alpha-->infinity is most interesting and most difficult to compute numerically. We derive exact expressions for both lim(N-->infinity) var(N)f and lim(alpha-->infinity), lim(N-->infinity) var(N)f.