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Tightness of Fluctuations of First Passage Percolation on Some Large Graphs

  • Itai BenjaminiEmail author
  • Ofer Zeitouni
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

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.

Keywords

First-passage Percolation (FPP) Lamp Light Bounded Degree Graphs Cayley Graph Subadditive Ergodic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Thanks to Pierre Pansu and Gabor Pete for very useful discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

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