Geodesic
Opinion propagation on social networks: a mathematical standpoint
H. Lavenant1 ; B. Maury2
1 Department of Mathematics, University of British Columbia, Vancouver BC Canada
2 DMA, École normale supérieure, CNRS, PSL University, 75005 Paris, France
ESAIM. Proceedings, Tome 67 (2020), pp. 285-335.

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These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric.
DOI : 10.1051/proc/202067016

H. Lavenant 1 ; B. Maury 2

1 Department of Mathematics, University of British Columbia, Vancouver BC Canada
2 DMA, École normale supérieure, CNRS, PSL University, 75005 Paris, France 
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H. Lavenant; B. Maury. Opinion propagation on social networks: a mathematical standpoint. ESAIM. Proceedings, Tome 67 (2020), pp. 285-335. doi : 10.1051/proc/202067016. http://geodesic.mathdoc.fr/articles/10.1051/proc/202067016/

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