Geodesic
Cone types and spectral radius of hyperbolic triangle groups and hyperbolic tessellations
Megan Howarth1 orcid ; Tatiana Nagnibeda1 orcid
1University of Geneva, Switzerland
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 477-493

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DOI

This paper is devoted to the study of tessellations of the hyperbolic plane, especially the ones associated to hyperbolic triangle groups Δ(l,m,n). We give a full description of the cone types of these graphs and show that their number depends only on the defining parameters of the group. We then use the cone type structure to provide estimates of the spectral radius for the simple random walk on these tessellations, from above and from below.
DOI : 10.4171/ggd/884
Classification : 05B45, 20F67, 05C81
Mots-clés : triangle groups, hyperbolic tessellations, cone types, spectral radius

Megan Howarth  1   ; Tatiana Nagnibeda  1

1 University of Geneva, Switzerland 
Megan Howarth; Tatiana Nagnibeda. Cone types and spectral radius of hyperbolic triangle groups and hyperbolic tessellations. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 477-493. doi: 10.4171/ggd/884
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     title = {Cone types and spectral radius of hyperbolic triangle groups and hyperbolic tessellations},
     journal = {Groups, geometry, and dynamics},
     pages = {477--493},
     year = {2025},
     volume = {19},
     number = {2},
     doi = {10.4171/ggd/884},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/884/}
}
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