Abstract
The theorem of Dekking and Host [Probab. Theor. Relat. Fields 90, 403–426 (1991)] regarding tightness around the mean of first passage percolation on the binary tree, from the root to a boundary of a ball, is generalized to a class of graphs which includes all lattices in hyperbolic spaces and the lamplighter graph over \(\mathbb{N}\). This class of graphs is closed under product with any bounded degree graph. Few open problems and conjectures are gathered at the end.
Itai Benjamini and Ofer Zeitouni
Both authors were supported by their respective Israel Science Foundation grants.
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Acknowledgements
Thanks to Pierre Pansu and Gabor Pete for very useful discussions.
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Benjamini, I., Zeitouni, O. (2012). Tightness of Fluctuations of First Passage Percolation on Some Large Graphs. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_6
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