Stable laws and products of positive random matrices
| dc.creator | Hennion, Hubert | |
| dc.creator | Hervé, Loic | |
| dc.date | 2008-01-24 | |
| dc.date.accessioned | 2026-07-07T08:56:12Z | |
| dc.date.available | 2026-07-07T08:56:12Z | |
| dc.description | Let $S$ be the multiplicative semigroup of $q\times q$ matrices with positive entries such that every row and every column contains a strictly positive element. Denote by $(X_n)_{n\geq1}$ a sequence of independent identically distributed random variables in $S$ and by $X^{(n)} = X_n ... X_1$, $ n\geq 1$, the associated left random walk on $S$. We assume that $(X_n)_{n\geq1}$ verifies the contraction property $¶(\bigcup_{n\geq1}[X^{(n)} \in S^\circ])>0$, where $S^\circ $ is the subset of all matrices which have strictly positive entries. We state conditions on the distribution of the random matrix $X_1$ which ensure that the logarithms of the entries, of the norm, and of the spectral radius of the products $X^{(n)}$, $n\ge 1$, are in the domain of attraction of a stable law. | |
| dc.description | 14 pages. To appear in Journal of Theoretical Probability | |
| dc.identifier | https://arxiv.org/abs/0801.3780 | |
| dc.identifier | http://arxiv.org/abs/0801.3780 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146529 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | 60F05 ; 60B99 ; 47B07 | |
| dc.title | Stable laws and products of positive random matrices | |
| dc.type | text |