Variance calculations and the Bessel kernel

Abstract

In the Laguerre ensembleof n xN 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, asN → ∞. Furthermore, this statistic often contains an additional parameter a for which the limit α → ∞ is most interesting and most difficult to compute numerically. We derive exact expressions for both lim_{N → ∞} var_N f and lim_{α → ∞}, lim_{N → ∞} var_N f.