Truncated linear statistics associated with the top eigenvalues of random matrices

Aurélien Grabsch ¹ Satya N. Majumdar ¹ Christophe Texier ¹

Journal of Statistical Physics, Springer Verlag, 2017, 167 (2), pp.234 – 259

Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues $P(\lambda_1,\cdots,\lambda_N)$, many important questions have been related to the study of linear statistics of eigenvalues $L=\sum_{i=1}^Nf(\lambda_i)$, where $f(\lambda)$ is a known function. We study here truncated linear statistics where the sum is restricted to the $N_1

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques