Emergent centrality in rank-based supplanting process

Kenji Shimomura; Yasuhiro Ishitsuka; Hiroki Ohta

doi:10.1103/physreve.107.034114

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arXiv · 2209.02336

Emergent centrality in rank-based supplanting process

Kenji Shimomura·Yasuhiro Ishitsuka·Hiroki Ohta

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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.

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Kenji Shimomura, Yasuhiro Ishitsuka, Hiroki Ohta. 2022-09-06. Emergent centrality in rank-based supplanting process. https://doi.org/10.1103/physreve.107.034114

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