Generating Random Vectors in (Z/pZ)^d Via an Affine Random Process
| dc.creator | Hildebrand, Martin | |
| dc.creator | McCollum, Joseph | |
| dc.date | 2007-01-20 | |
| dc.date | 2007-11-26 | |
| dc.date.accessioned | 2026-07-07T08:44:43Z | |
| dc.date.available | 2026-07-07T08:44:43Z | |
| dc.description | This paper considers some random processes of the form X_{n+1}=TX_n+B_n (mod p) where B_n and X_n are random variables over (Z/pZ)^d and T is a fixed d x d integer matrix which is invertible over the complex numbers. For a particular distribution for B_n, this paper improves results of Asci to show that if T has no complex eigenvalues of length 1, then for integers p relatively prime to det(T), order (log p)^2 steps suffice to make X_n close to uniformly distributed where X_0 is the zero vector. This paper also shows that if T has a complex eigenvalue which is a root of unity, then order p^b steps are needed for X_n to get close to uniform where b is a value which may depend on T and X_0 is the zero vector. | |
| dc.description | This version incorporates some changes suggested by a referee and is the final pre-publication version. The published version is to appear in the Journal of Theoretical Probability | |
| dc.identifier | https://arxiv.org/abs/math/0701570 | |
| dc.identifier | http://arxiv.org/abs/math/0701570 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142758 | |
| dc.subject | Probability | |
| dc.subject | 60B15 (primary); 60J10 (secondary) | |
| dc.title | Generating Random Vectors in (Z/pZ)^d Via an Affine Random Process | |
| dc.type | text |