## Electronic Communications in Probability

### Connected allocation to Poisson points in $\mathbb{R}^2$

Maxim Krikun

#### Abstract

This note answers one question in [1] concerning the connected allocation for the Poisson process in $\mathbb{R}^2$. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to the halfplane. A picture of a numerically simulated example is included.

#### Article information

Source
Electron. Commun. Probab., Volume 12 (2007), paper no. 15, 140-145.

Dates
Accepted: 8 May 2007
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465224958

Digital Object Identifier
doi:10.1214/ECP.v12-1268

Mathematical Reviews number (MathSciNet)
MR2318161

Zentralblatt MATH identifier
1128.60012

Keywords
Poisson process Riemann map

Rights
Krikun, Maxim. Connected allocation to Poisson points in $\mathbb{R}^2$. Electron. Commun. Probab. 12 (2007), paper no. 15, 140--145. doi:10.1214/ECP.v12-1268. https://projecteuclid.org/euclid.ecp/1465224958