Quermass-interaction process with convex compact grains

Kateřina Helisová; Jakub Staněk

Applications of Mathematics (2016)

  • Volume: 61, Issue: 4, page 463-487
  • ISSN: 0862-7940

Abstract

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The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.

How to cite

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Helisová, Kateřina, and Staněk, Jakub. "Quermass-interaction process with convex compact grains." Applications of Mathematics 61.4 (2016): 463-487. <http://eudml.org/doc/283402>.

@article{Helisová2016,
abstract = {The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.},
author = {Helisová, Kateřina, Staněk, Jakub},
journal = {Applications of Mathematics},
keywords = {attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability; attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability},
language = {eng},
number = {4},
pages = {463-487},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quermass-interaction process with convex compact grains},
url = {http://eudml.org/doc/283402},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Helisová, Kateřina
AU - Staněk, Jakub
TI - Quermass-interaction process with convex compact grains
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 463
EP - 487
AB - The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.
LA - eng
KW - attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability; attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability
UR - http://eudml.org/doc/283402
ER -

References

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