Limit theorems for radial random walks on pxq-matrices as p tends to infinity
| dc.creator | Rösler, Margit | |
| dc.creator | Voit, Michael | |
| dc.date | 2007-03-18 | |
| dc.date.accessioned | 2026-07-07T07:52:35Z | |
| dc.date.available | 2026-07-07T07:52:35Z | |
| dc.description | The radial probability measures on $R^p$ are in a one-to-one correspondence with probability measures on $[0,\infty[$ by taking images of measures w.r.t. the Euclidean norm mapping. For fixed $ν\in M^1([0,\infty[)$ and each dimension p, we consider i.i.d. $R^p$-valued random variables $X_1^p,X_2^p,...$ with radial laws corresponding to $ν$ as above. We derive weak and strong laws of large numbers as well as a large deviation principle for the Euclidean length processes $S_k^p:=\|X_1^p+...+X_k^p\|$ as k,p\to\infty in suitable ways. In fact, we derive these results in a higher rank setting, where $R^p$ is replaced by the space of $p\times q$ matrices and $[0,\infty[$ by the cone $Π_q$ of positive semidefinite matrices. Proofs are based on the fact that the $(S_k^p)_{k\ge 0}$ form Markov chains on the cone whose transition probabilities are given in terms Bessel functions $J_μ$ of matrix argument with an index $μ$ depending on p. The limit theorems follow from new asymptotic results for the $J_μ$ as $μ\to \infty$. Similar results are also proven for certain Dunkl-type Bessel functions. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703520 | |
| dc.identifier | http://arxiv.org/abs/math/0703520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125933 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Probability | |
| dc.subject | 43A85; 33C67; 60F; 43A62; 60B12 | |
| dc.title | Limit theorems for radial random walks on pxq-matrices as p tends to infinity | |
| dc.type | text |