Note on the Lilypond model

C Cotar, S Volkov

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


We consider some generalizations of the germ-grain growing model studied by Daley, Mallows and Shepp (2000). In this model, a realization of a Poisson process on a line with points X-i is fixed. At time zero, simultaneously at each Xi, a circle (grain) starts growing at the same speed. It grows until it touches another grain, and then it stops, The question is whether the point zero is eventually covered by some circle. In our note we expand this model in the following three directions. We study: a one-sided growth model with a fixed number of circles; a grain-growth model on a regular tree; and a grain-growth model on a line with non-Poisson distributed centres of the circles.
Translated title of the contributionNote on the Lilypond model
Original languageEnglish
Pages (from-to)325 - 339
Number of pages15
JournalAdvances in Applied Probability
Volume36 (2)
Publication statusPublished - Jun 2004

Bibliographical note

Publisher: Applied Probability Trust
Other identifier: IDS Number: 827RT


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