Higher-order derivatives of first-passage percolation with respect to the environment
Ivan Matic, Rados Radoicic, Dan Stefanica
公開日: 2025/4/11
Abstract
We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. 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.