# Divergence of shape fluctuation for general distributions in first passage percolation

## TL;DR

This paper extends the understanding of shape fluctuation divergence in first passage percolation from Bernoulli distributions to a broader class of distributions, showing that divergence is a general phenomenon.

## Contribution

It generalizes previous results by proving divergence of shape fluctuations for a wide range of distributions in first passage percolation.

## Key findings

- Shape fluctuation diverges for general distributions.
- Extends divergence results beyond Bernoulli cases.
- Supports the universality of fluctuation divergence in first passage percolation.

## Abstract

We study the shape fluctuation in the first passage percolation on $\mathbb{Z}^d$. It is known that it diverges when the distribution obeys Bernoulli in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. Probab. Theory. Related. Fields. 136(2) 298-320, 2006]. In this paper, we extend the result to general distributions.