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Perfect Sampling for Hard Spheres from Strong Spatial Mixing

Authors Konrad Anand, Andreas Göbel, Marcus Pappik, Will Perkins

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Author Details

Konrad Anand
  • Queen Mary, University of London, UK
Andreas Göbel
  • Hasso Plattner Institute, University of Potsdam, Germany
Marcus Pappik
  • Hasso Plattner Institute, University of Potsdam, Germany
Will Perkins
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA

Funding

  • Anand, Konrad: funded by a studentship from Queen Mary, University of London.
  • Göbel, Andreas: funded by the project PAGES (project No. 467516565) of the German Research Foundation (DFG).
  • Pappik, Marcus: funded by the HPI Research School on Data Science and Engineering.
  • Perkins, Will: supported in part by NSF grant DMS-2309958.

Acknowledgements

We thank Mark Jerrum for very helpful discussions on this topic.

Cite AsGet BibTex

Konrad Anand, Andreas Göbel, Marcus Pappik, and Will Perkins. Perfect Sampling for Hard Spheres from Strong Spatial Mixing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.38

Abstract

We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials.

Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • perfect sampling
  • hard-sphere model
  • Gibbs point processes

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