Zeros of random polynomials on C^m
| dc.creator | Bloom, Thomas | |
| dc.creator | Shiffman, Bernard | |
| dc.date | 2006-05-30 | |
| dc.date.accessioned | 2026-07-07T08:42:27Z | |
| dc.date.available | 2026-07-07T08:42:27Z | |
| dc.description | For a regular compact set $K$ in $C^m$ and a measure $μ$ on $K$ satisfying the Bernstein-Markov inequality, we consider the ensemble $P_N$ of polynomials of degree $N$, endowed with the Gaussian probability measure induced by $L^2(μ)$. We show that for large $N$, the simultaneous zeros of $m$ polynomials in $P_N$ tend to concentrate around the Silov boundary of $K$; more precisely, their expected distribution is asymptotic to $N^m μ_{eq}$, where $μ_{eq}$ is the equilibrium measure of $K$. For the case where $K$ is the unit ball, we give scaling asymptotics for the expected distribution of zeros as $N\to\infty$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605739 | |
| dc.identifier | http://arxiv.org/abs/math/0605739 | |
| dc.identifier | Math. Res. Lett. 14 (2007), 469-479 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141967 | |
| dc.subject | Complex Variables | |
| dc.subject | Probability | |
| dc.title | Zeros of random polynomials on C^m | |
| dc.type | text |