Transversal fluctuations for a first passage percolation model

@article{Bakhtin2019TransversalFF,
title={Transversal fluctuations for a first passage percolation model},
author={Yuri Bakhtin and Wei Wu},
journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
year={2019}
}
• Published 19 May 2016
• Mathematics
• Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
We introduce a new first passage percolation model in a Poissonian environment on $\mathbb{R}^{2}$. In this model, the action of a path depends on the geometry of the path and the travel time. We prove that the transversal fluctuation exponent for point-to-line action minimizers is at least $3/5$.
1 Citations

Figures from this paper

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The results shed some light on the Euclidean first-passage process but also raise some theoretical questions about the scaling laws and the derivation of the exponent values and also whether a model can be constructed with maximal wandering, or non-Gaussian travel fluctuations, while embedded in space.

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