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Quermass-interaction process with convex compact grains

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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.

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Author information

Authors and Affiliations

  1. Czech Technical University in Prague, Faculty of Electrical Engineering Department of Mathematics, Technická 2, 166 27, Praha 6, Czech Republic

    Kateřina Helisová

  2. Department of Mathematics Education, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jakub Staněk

Authors
  1. Kateřina Helisová
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  2. Jakub Staněk
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Corresponding author

Correspondence to Kateřina Helisová.

Additional information

The research was supported by Czech Science Foundation, grant No. 13-05466P.

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Helisová, K., Staněk, J. Quermass-interaction process with convex compact grains. Appl Math 61, 463–487 (2016). https://doi.org/10.1007/s10492-016-0142-x

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