Electronic Communications in Probability

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

Maxim Krikun

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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

Permanent link to this document
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

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Poisson process Riemann map

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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