Emergent centrality in rank-based supplanting process

TL;DR

This paper introduces a stochastic model inspired by macaque social dynamics, analyzing how agent rank influences centrality measures and symmetry breaking, with implications for understanding rank-based interactions.

Contribution

It presents a novel rank-dependent stochastic process and a new measure, overlap centrality, to analyze symmetry breaking in rank-based agent interactions.

Findings

Overlap centrality correlates with agent rank in zero-supplanting limit.

The model demonstrates symmetry breaking in agent interactions.

A singularity in correlation is identified with Potts energy interactions.

Abstract

We propose a stochastic process of interacting many agents, which is inspired by rank-based supplanting dynamics commonly observed in a group of Japanese macaques. In order to characterize the breaking of permutation symmetry with respect to agents' rank in the stochastic process, we introduce a rank-dependent quantity, overlap centrality, which quantifies how often a given agent overlaps with the other agents. We give a sufficient condition in a wide class of the models such that overlap centrality shows perfect correlation in terms of the agents' rank in zero-supplanting limit. We also discuss a singularity of the correlation in the case of interaction induced by a Potts energy.