The Annals of Applied Probability

Scaling limits for continuous opinion dynamics systems

Giacomo Como and Fabio Fagnani

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Abstract

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system’s mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 4 (2011), 1537-1567.

Dates
First available in Project Euclid: 8 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1312818844

Digital Object Identifier
doi:10.1214/10-AAP739

Mathematical Reviews number (MathSciNet)
MR2857456

Zentralblatt MATH identifier
1235.60136

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 91D30: Social networks 93A15: Large scale systems

Keywords
Multi-agent systems social networks opinion dynamics bounded confidence scaling limits probability-measure-valued ODEs

Citation

Como, Giacomo; Fagnani, Fabio. Scaling limits for continuous opinion dynamics systems. Ann. Appl. Probab. 21 (2011), no. 4, 1537--1567. doi:10.1214/10-AAP739. https://projecteuclid.org/euclid.aoap/1312818844


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