Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 4, 615--633

Products of I.I.D. Random Nonnegative Matrices: Their Skeletons and Convergence in Distribution

G\"oran H\"ogn\"as, \AA bo Akademi University,  Finland
Arunava Mukherjea, University of South Florida, Tampa,  USA

SUMMARY. Under mild conditions, it is shown that if $X_1,X_2,\dots$, is a sequence of $d$ by $d$ random nonnegative i.i.d.\ matrices, then the convergence in distribution of products $X_1X_2\dotsm X_n$ essentially depends on the skeletons of $X_1$. (Two $d$ by $d$ nonnegative matrices have the same skeleton if their positive entries appear on identical positions.

AMS (2000) subject classification. 60B15, 60B10, 20M20, 15A51.

Key words and phrases. Random matrices, convergence in distribution, skeleton of a matrix.

Full paper (PDF)