Convergence of random measures in geometric probability
| dc.creator | Penrose, Mathew D. | |
| dc.date | 2005-08-24 | |
| dc.date.accessioned | 2026-07-07T05:22:39Z | |
| dc.date.available | 2026-07-07T05:22:39Z | |
| dc.description | Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $ν_n = \sum_i ξ_i $, where $ξ_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near $X_i$. Technically, this means here that $ξ_i$ stabilizes with a suitable power-law decay of the tail of the radius of stabilization. For bounded test functions $f$ on $R^d$, we give a law of large numbers and central limit theorem for $ν_n(f)$. The latter implies weak convergence of $ν_n(\cdot)$, suitably scaled and centred, to a Gaussian field acting on bounded test functions. The general result is illustrated with applications including the volume and surface measure of germ-grain models with unbounded grain sizes. | |
| dc.description | 51 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508464 | |
| dc.identifier | http://arxiv.org/abs/math/0508464 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76141 | |
| dc.subject | Probability | |
| dc.subject | 60D05, 60G57, 60F05, 60F25, 52A22 | |
| dc.title | Convergence of random measures in geometric probability | |
| dc.type | text |