Large deviations for the zero set of an analytic function with diffusing coefficients
| dc.creator | Hough, J. Ben | |
| dc.date | 2005-10-11 | |
| dc.date.accessioned | 2026-07-07T06:47:23Z | |
| dc.date.available | 2026-07-07T06:47:23Z | |
| dc.description | The "hole probability" that the zero set of the time dependent planar Gaussian analytic function f(z,t) = sum_(n=0)^infty a_n(t) z^n/sqrt(n!), where a_n(t) are i.i.d. complex valued Ornstein-Uhlenbeck processes, does not intersect a disk of radius R for all 0<t<T decays like exp(-Te^(cR^2)). This result sharply differentiates the zero set of f from a number of canonical evolving planar point processes. For example, the hole probability of the perturbed lattice model {sqrtπ(m,n) + c zeta_{m,n}: m,n integers} where zeta_(m,n) are i.i.d. Ornstein-Uhlenbeck processes decays like exp(-cTR^4). This stark contrast is also present in the "overcrowding probability" that a disk of radius R contains at least N zeros for all 0<t<T. | |
| dc.description | 24 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0510237 | |
| dc.identifier | http://arxiv.org/abs/math/0510237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103635 | |
| dc.subject | Probability | |
| dc.subject | Complex Variables | |
| dc.subject | 60G15, 60G70 | |
| dc.title | Large deviations for the zero set of an analytic function with diffusing coefficients | |
| dc.type | text |