From Kreweras walks to branching perimeter processes of percolated triangulations

Renan Gross; Emmanuel Kammerer; Frederik Ravn Klausen

From Kreweras walks to branching perimeter processes of percolated triangulations

Combinatorics 2026-07-30 v1 Mathematical Physics Probability

Authors: Renan Gross , Emmanuel Kammerer , Frederik Ravn Klausen

Abstract

In this note, using a result of Bernardi, Holden and Sun, we give an explicit geometric relation between the perimeter of the peeling process along the percolation interface of a triangulation, and the corresponding Kreweras walk. The relation naturally extends to the branching peeling exploration. This sheds light on the relation between the growth-fragmentation process and correlated Brownian excursions discovered by Da Silva, Powell and Watson.

Keywords

percolation triangulations Kreweras walks branching processes Brownian excursions

Cite

@article{arxiv.2607.28566,
  title  = {From Kreweras walks to branching perimeter processes of percolated triangulations},
  author = {Renan Gross and Emmanuel Kammerer and Frederik Ravn Klausen},
  journal= {arXiv preprint arXiv:2607.28566},
  year   = {2026}
}

Comments

16 pages, 8 figures