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8 - Ends of Branching Random Walks on Planar Hyperbolic Cayley Graphs

Published online by Cambridge University Press:  20 July 2017

Lorenz A. Gilch
Affiliation:
Know Center GmbH, Inffeldgasse 13, A-8010 Graz, Austria
Sebastian Müller
Affiliation:
Aix Marseille University, CNRS, Centrale Marseille, I2M, Marseille, France
Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Maura Salvatori
Affiliation:
Università degli Studi di Milano
Ecaterina Sava-Huss
Affiliation:
Cornell University, New York
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Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] D., Aldous and R., Lyons. Processes on unimodular random networks. Electron. J. Probab., 12:no. 54, 1454–508, 2007.Google Scholar
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[3] I., Benjamini and S., Müller. On the trace of branching random walks. Groups Geom. Dyn., 2(2):231–47, 2012.Google Scholar
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[5] D., Calegari. The ergodic theory of hyperbolic groups. Contemp. Math, pages 15–52, 2013.Google Scholar
[6] E., Candellero, L.A., Gilch, and S., Müller. Branching random walks on free products of groups. Proc. Lond. Math. Soc. (3), 6(6):1085–120, 2012.Google Scholar
[7] E., Candellero and M. I., Roberts. The number of ends of critical branching random walks. http://arxiv.org/abs/1401.0429, 2014.
[8] N., Gantert and S., Müller. The critical branching Markov chain is transient. Markov Process. and Rel. Fields., 12:805–14, 2007.Google Scholar
[9] S., Gouëzel. Local limit theorem for symmetric random walks in Gromovhyperbolic groups. J. Amer. Math. Soc., 3(3):893–928, 2014.Google Scholar
[10] S., Gouëzel and S. P., Lalley. Random walks on co-compact Fuchsian groups. Ann. Sci. Éc. Norm. Supér. (4), 1(1):129–73, 2013.Google Scholar
[11] I., Hueter and S. P., Lalley. Anisotropic branching random walks on homogeneous trees. Probab. Th. Rel. Fields, 1(1):57–88, 2000.Google Scholar
[12] R., Lyons, with Y., Peres. Probability on Trees and Networks. Cambridge University press, In preparation. Current version available at http://mypage.iu.edu/~rdlyons/.
[13] S., Müller. Interacting growth processes and invariant percolation. Ann. Appl. Prob., 1(1):268–86, 2015.Google Scholar
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