Transversal fluctuations for a first passage percolation model

TL;DR

This paper introduces a new first passage percolation model in a Poisson environment and establishes a lower bound of 3/5 for the transversal fluctuation exponent of action minimizers.

Contribution

It presents a novel percolation model and provides the first rigorous lower bound for the transversal fluctuation exponent in this setting.

Findings

Transversal fluctuation exponent is at least 3/5.

New first passage percolation model in Poissonian environment.

Insights into geometric behavior of action minimizers.

Abstract

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 $3/5$.