Variance Calculations and the Bessel Kernel

In the Laguerre ensemble of N ×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 varN f , as N → ∞. Furthermore, this statistic often contains an additional parameter α for which the limit α → ∞ is most interesting and most difficult to compute numerically. We derive exact expressions for both limN→∞ varN f and limα→∞ limN→∞ varN f .