On the singularity probability of discrete random matrices
| dc.creator | Bourgain, Jean | |
| dc.creator | Vu, Van | |
| dc.creator | Wood, Philip Matchett | |
| dc.date | 2009-05-04 | |
| dc.date.accessioned | 2026-07-07T13:11:32Z | |
| dc.date.available | 2026-07-07T13:11:32Z | |
| dc.description | Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best upper bound of $(3/4 + o(1))^n$ proven by Tao and Vu in arXiv:math/0501313v2. This paper follows a similar approach to the Tao and Vu result, including using a variant of their structure theorem. We also extend this type of exponential upper bound on the probability that a random matrix is singular to a large class of discrete random matrices taking values in the complex numbers, where the entries are independent but are not necessarily identically distributed. | |
| dc.description | 45 pages, two figures | |
| dc.identifier | https://arxiv.org/abs/0905.0461 | |
| dc.identifier | http://arxiv.org/abs/0905.0461 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229309 | |
| dc.subject | Combinatorics | |
| dc.subject | 15A52 | |
| dc.title | On the singularity probability of discrete random matrices | |
| dc.type | text |