Translator Disclaimer
VOL. 87 | 2021 Divergence of non-random fluctuation for Euclidean first-passage percolation
Shuta Nakajima

Editor(s) Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai

## Abstract

The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [11] that for a particular asymptotic direction, it diverges in a lattice first passage percolation with an explicit lower bound. In this paper, we discuss the non-random fluctuation in Euclidean first passage percolations and show that it diverges in dimension $d \geq 2$ in this model also. Compared with the result in [11], the present result is proved for any direction and improves the lower bound.

## Information

Published: 1 January 2021
First available in Project Euclid: 20 January 2022

Digital Object Identifier: 10.2969/aspm/08710363

Subjects:
Primary: 60K37
Secondary: 60K35 , 82A51 , 82D30

Keywords: First-passage percolation , random environment