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DOI: 10.4230/LIPIcs.AofA.2026.10

Gibbs Partitions and Lattice Paths

Authors: Niccolò Bosio, Markus Kuba, and Benedikt Stufler

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)

Abstract

We study a Gibbs partition model (composition scheme) under a new condition on the component weights, leading to a previously unobserved regime for the number of components. We establish a condensation phenomenon producing a unique giant component, and prove a Cox process limit describing a sublinear power-law growth of sizes of non-maximal components. Our results are motivated by applications to lattice paths and random walks, including simple random walks in the cube, Delannoy paths, pairs of Dyck bridges, urn models and card guessing games.

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Niccolò Bosio, Markus Kuba, and Benedikt Stufler. Gibbs Partitions and Lattice Paths. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 10:1-10:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bosio_et_al:LIPIcs.AofA.2026.10,
  author =	{Bosio, Niccol\`{o} and Kuba, Markus and Stufler, Benedikt},
  title =	{{Gibbs Partitions and Lattice Paths}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{10:1--10:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.10},
  URN =		{urn:nbn:de:0030-drops-262814},
  doi =		{10.4230/LIPIcs.AofA.2026.10},
  annote =	{Keywords: Gibbs partitions, composition schemes, lattice paths, random walks, condensation}
}

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Gibbs Partitions and Lattice Paths

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