New results on the convergence of random matrices

This paper extends the previous convergence results in Cerqueti and Costantini (2008) to a more general case using larger normed set of functions. In this regard, the weight-based convergence of the random matrices and their generalized eigenvalues is obtained under less restrictive requirements for the weights. This is an Accepted Manuscript of an article published by Taylor & Francis in Statistics on 10 January 2012, available online: http://www.tandfonline.com/10.1080/02331888.2011.648639