The geometry of a critical percolation cluster on the UIPT. (English. French summary) Zbl 1434.60292

Summary: We consider a critical Bernoulli site percolation on the uniform infinite planar triangulation. We study the tail distributions of the peeling time, perimeter, and volume of the hull of a critical cluster. The exponents obtained here differ by a factor 2 from those computed previously by O. Angel and N. Curien [Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 2, 405–431 (2015; Zbl 1315.60105)] in the case of critical site percolation on the uniform infinite half-plane triangulation.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C80 Random graphs (graph-theoretic aspects)


Zbl 1315.60105
Full Text: DOI arXiv Euclid


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