## Electronic Communications in Probability

### The greedy walk on an inhomogeneous Poisson process

#### Abstract

The greedy walk is a deterministic walk that always moves from its current position to the nearest not yet visited point. In this paper we consider the greedy walk on an inhomogeneous Poisson point process on the real line. We prove that the property of visiting all points of the point process satisfies a $0$–$1$ law and determine explicit sufficient and necessary conditions on the mean measure of the point process for this to happen. Moreover, we provide precise results on threshold functions for the property of visiting all points.

#### Article information

Source
Electron. Commun. Probab. Volume 23 (2018), paper no. 14, 11 pp.

Dates
Accepted: 14 February 2018
First available in Project Euclid: 27 February 2018

https://projecteuclid.org/euclid.ecp/1519722244

Digital Object Identifier
doi:10.1214/18-ECP119

#### Citation

Gabrysch, Katja; Thörnblad, Erik. The greedy walk on an inhomogeneous Poisson process. Electron. Commun. Probab. 23 (2018), paper no. 14, 11 pp. doi:10.1214/18-ECP119. https://projecteuclid.org/euclid.ecp/1519722244

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