**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.