Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems

TL;DR

This paper introduces a minimal model of two coupled agents with memory, revealing emergent anomalous diffusion, non-Gaussian distributions, and new universality classes in coupled stochastic processes, advancing understanding of multi-agent transport phenomena.

Contribution

The study uncovers new universality classes for coupled random walks with memory, characterized by unique scaling laws and distributional properties not previously reported.

Findings

Identification of distinct anomalous diffusion regimes

Discovery of non-Gaussian position distributions

Revelation of compressed exponential encounter statistics

Abstract

Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being attracted to the trails left by one another. This system is inspired by, but not limited to, pheromone-guided insect navigation. The coupling of self-avoidance and attraction generates rich emergent behavior, including distinct anomalous diffusion regimes, non-Gaussian position distributions, and compressed exponential encounter statistics. Most notably, we identify new universality classes for coupled random walks, characterized by unique scaling laws and distributional properties that, to our knowledge, have not been previously reported. These findings advance the theoretical understanding of coupled stochastic processes with memory and interaction feedback, providing a framework for exploring transport phenomena in a broad range of multi-agent systems beyond biological contexts.