Two lilypond systems of finite line-segments

• Autorzy: Daley D. J. , Ebert S. , Last G.
• Języki publikacji: EN

Abstrakty

EN

The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points P = {P_i} in R² with which are associated directions {θ_i}. At time zero, for each and every i, a line-segment L_i starts growing at unit rate around the point P_i in the direction θ_i, the point P_i remaining at the centre of L_i; each line-segment, under Model 1, ceases growth when one of its ends hits another line, while under Model 2, its growth ceases either when one of its ends hits another line or when it is hit by the growing end of some other line. The paper shows that these procedures are well defined and gives constructive algorithms to compute the half-lengths R_i of all L_i. Moreover, it specifies assumptions under which stochastic versions, i.e. models based on point processes, exist. Afterwards, it deals with the question as to whether there is percolation in Model 1. The paper concludes with a section containing several conjectures and final remarks.

Słowa kluczowe

EN

hardcore model; point process; cluster; percolation; lilypond growth protocol

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 221--246
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Daley D. J.

• Department of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia

autor

Ebert S.

• Karlsruher Institut für Technologie, 76128 Karlsruhe, Germany

autor

Last G.

• Karlsruher Institut für Technologie, 76128 Karlsruhe, Germany

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).