Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots

Understand

Invariant ensembles of random matrices are characterized by the distribution of their eigenvalues $\{\lambda_1,\cdots,\lambda_N\}$.

• We study the distribution of truncated linear statistics of the form $\tilde{L}=\sum_{i=1}^p f(\lambda_i)$ with $p<N$.
• This problem has been considered by us in a previous paper when the $p$ eigenvalues are further constrained to be the largest ones (or the smallest).
• In this second paper we consider the same problem without this restriction which leads to a rather different analysis.