Non-uniqueness Phase of Percolation on Reflection Groups in $${\mathbb {H}^3}$$ H 3

Jan Czajkowski ()
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Jan Czajkowski: Wrocław University of Science and Technology

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2534-2575

Abstract: Abstract We consider Bernoulli bond and site percolation on Cayley graphs of reflection groups in the three-dimensional hyperbolic space $${\mathbb {H}^3}$$ H 3 corresponding to a very large class of Coxeter polyhedra. In such setting, we prove the existence of a non-empty non-uniqueness percolation phase, i.e. that $$p_c

Keywords: Percolation; Coxeter groups; Hyperbolic space; Spectral radius; Gabber’s lemma; Growth series; 82B43; 20F55 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01313-9

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