Journal of Applied Probability

Distribution of the smallest visited point in a greedy walk on the line

Katja Gabrysch

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We consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.

Article information

J. Appl. Probab. Volume 53, Number 3 (2016), 880-887.

First available in Project Euclid: 13 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Poisson point process greedy walk


Gabrysch, Katja. Distribution of the smallest visited point in a greedy walk on the line. J. Appl. Probab. 53 (2016), no. 3, 880--887.

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