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PreprintCC BY 4.0arXiv

Kruskal-style algorithm for Boltzmann equation molecule reduction

  • Yvain Bruned
  • Valentin Clarisse
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Abstract

We are interested in the molecule reduction algorithm used by Deng, Hani and Ma. This algorithm allows them to establish a rigidity theorem, which plays a central role in the long-time derivation of the Boltzmann equation using the hard-sphere dynamics. In the present article, we show that this algorithm is a graph traversal algorithm of Kruskal type, and we prove that it constructs a Kruskal spanning tree of the input molecule.

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Cite

BibTeXRIS
BibTeX
@misc{bruned2026kruskalstyle,
  title = {{Kruskal-style algorithm for Boltzmann equation molecule reduction}},
  author = {Yvain Bruned and Valentin Clarisse},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38061},
  eprint = {2609.38061},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38061},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Kruskal-style algorithm for Boltzmann equation molecule reduction
AU  - Yvain Bruned
AU  - Valentin Clarisse
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38061
UR  - https://arxiv.org/abs/2609.38061
AB  - We are interested in the molecule reduction algorithm used by Deng, Hani and Ma. This algorithm allows them to establish a rigidity theorem, which plays a central role in the long-time derivation of the Boltzmann equation using the hard-sphere dynamics. In the present article, we show that this algorithm is a graph traversal algorithm of Kruskal type, and we prove that it constructs a Kruskal spanning tree of the input molecule.
ER  -