Journal of Applied Probability

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

Katja Gabrysch

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Abstract

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

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

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1476370782

Mathematical Reviews number (MathSciNet)
MR3570100

Zentralblatt MATH identifier
1351.60060

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

Keywords
Poisson point process greedy walk

Citation

Gabrysch, Katja. Distribution of the smallest visited point in a greedy walk on the line. J. Appl. Probab. 53 (2016), no. 3, 880--887.https://projecteuclid.org/euclid.jap/1476370782


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