### Speaker

Dr
Thi Da Cam PHAM
(Institut Denis Poisson, Faculté des sciences, Tours, France.)

### Description

Inspired by a recent paper of I. Grama, E. Le Page and M. Peigné, we consider a
sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d \times d -$ matrices with non negative entries and study the fluctuations of the process $(\log | g_n ... g_1 x ) {n \geq 1}$ for any non-zero vector $x$ in $R^d$ with non-negative coordinates.
Our method involves approximating this process by a martingale and
studying harmonic functions for its restriction to the upper half line.
Under certain conditions, the probability for this process to stay
in the upper half real line up to time $n$ decreases as
$c \over \sqrt n$ for some positive constant $c$.

### Primary author

Dr
Thi Da Cam PHAM
(Institut Denis Poisson, Faculté des sciences, Tours, France.)