Abstract
It is shown that the maximum of the height of the Gaussian free field in a ball of a two dimensional hyperbolic lattice, grows linearly with the radius, while only as a square root of the radius on higher dimensional hyperbolic lattices.
Keywords
- Gaussian Free Field (GFF)
- Hyperbolic Lattice
- Random Lipschitz Functions
- Euclidean Lattice
- Exponential Volume Growth
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Acknowledgements
Thanks to Omer Angel, Alessandro Carderi and Yuval Peres. Sergey Khristo helped with the writing and figures.
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© 2014 Springer International Publishing Switzerland
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Benjamini, I. (2014). Gaussian Free Field on Hyperbolic Lattices. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_2
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DOI: https://doi.org/10.1007/978-3-319-09477-9_2
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Online ISBN: 978-3-319-09477-9
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