A shape theorem for Riemannian first-passage percolation

T. LaGatta; J. Wehr

doi:10.1063/1.3409344

A shape theorem for Riemannian first-passage percolation

T. LaGatta, J. Wehr

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in ^Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.

Original language	English (US)
Article number	024005JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	5
DOIs	https://doi.org/10.1063/1.3409344
State	Published - May 2010

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.",

author = "T. LaGatta and J. Wehr",

note = "Funding Information: The authors thank K. Gaw{\c e}dzki and ENS-Lyon for hospitality during the Spring of 2007 when this project was started. T.L. was supported by NSF VIGRE Grant No. at the University of Arizona. J.W. was supported by NSF Grant No. . Copyright: Copyright 2012 Elsevier B.V., All rights reserved.",

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N2 - Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.

AB - Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.

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A shape theorem for Riemannian first-passage percolation

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