Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Lanchier, Nicolas, Mercer, Max
Institution: Arizona State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4391591193