Higher-order derivatives of first-passage percolation with respect to the environment
Probability
2026-05-14 v4
Abstract
We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on . We show that the variance of the passage time can be expressed in terms of these derivatives. We further analyze their structure and establish several fundamental properties and bounds.
Cite
@article{arxiv.2504.08935,
title = {Higher-order derivatives of first-passage percolation with respect to the environment},
author = {Ivan Matic and Rados Radoicic and Dan Stefanica},
journal= {arXiv preprint arXiv:2504.08935},
year = {2026}
}