Limiting behavior of a kindness model

Nicolas Lanchier and Max Mercer

Statistics & Probability Letters, 2024, vol. 214, issue C

Abstract: This paper is concerned with a stochastic model for the spread of kindness across a social network. Individuals are located on the vertices of a general finite connected graph, and are characterized by their kindness belief. Each individual, say x, interacts with each of its neighbors, say y, at rate one. The interactions can be kind or unkind, with kind interactions being more likely when the kindness belief of the sender x is high. In addition, kind interactions increase the kindness belief of the recipient y, whereas unkind interactions decrease its kindness belief. The system also depends on two parameters modeling the impact of kind and unkind interactions, respectively. We prove that, when kind interactions have a larger impact than unkind interactions, the system converges to the purely kind configuration with probability tending to one exponentially fast in the large population limit.

Keywords: Interacting particle systems; Optional stopping theorem; Kindness belief (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110205

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