Large deviations of cascade processes on graphs

TL;DR

This paper introduces an efficient method to analyze rare, non-typical cascade trajectories in irreversible dynamical processes on large graphs, advancing understanding of out-of-equilibrium phenomena.

Contribution

The paper presents a novel, scalable approach to identify and analyze optimized trajectories of cascade processes in large systems with irreversible rules.

Findings

Method efficiently finds optimized cascade trajectories

Applicable to a wide class of irreversible dynamical rules

Enables analysis of rare events in large-scale systems

Abstract

Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical trajectories, which can be crucial for the understanding of the out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems.