Geodesic
Asymptotic Properties of Collective-Rearrangement Algorithms
Hirsch, Christian1 ; Gaiselmann, Gerd1 ; Schmidt, Volker1
1 Institute of Stochastics, Ulm University, 89069 Ulm, Germany.
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 236-250

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We analyze asymptotic properties of collective-rearrangement algorithms being a class of dense packing algorithms. Traditionally, they transform finite systems of (possibly overlapping) particles into non-overlapping configurations by collective rearrangement of particles in finitely many steps. We consider the convergence of such algorithms for not necessarily finite input data, which means that the configuration of particles in any bounded sampling window remains unchanged after finitely many rearrangement steps. More precisely, we derive sufficient conditions implying the convergence of such algorithms when a stationary process of particles is used as input. We also provide numerical results and present an application in computational materials science.

Reçu le :
DOI : 10.1051/ps/2014026
Classification : 60K35, 60D05, 82C22
Keywords: Asymptotics, force-biased algorithm, collective rearrangement, random sphere-packing, stationary particle system

Hirsch, Christian 1 ; Gaiselmann, Gerd 1 ; Schmidt, Volker 1

1 Institute of Stochastics, Ulm University, 89069 Ulm, Germany. 
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     title = {Asymptotic {Properties} of {Collective-Rearrangement} {Algorithms}},
     journal = {ESAIM: Probability and Statistics},
     pages = {236--250},
     publisher = {EDP-Sciences},
     volume = {19},
     year = {2015},
     doi = {10.1051/ps/2014026},
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     zbl = {1348.60028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2014026/}
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Hirsch, Christian; Gaiselmann, Gerd; Schmidt, Volker. Asymptotic Properties of Collective-Rearrangement Algorithms. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 236-250. doi: 10.1051/ps/2014026

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