dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Estrada Rodríguez, Gissell
dc.contributor.author
Modrego Ríos, Román
dc.date.accessioned
2025-11-06T08:53:29Z
dc.date.available
2025-11-06T08:53:29Z
dc.date.issued
2025-06-17
dc.identifier
https://hdl.handle.net/2117/445508
dc.identifier
PRISMA-195151
dc.identifier.uri
https://hdl.handle.net/2117/445508
dc.description.abstract
This bachelor’s thesis explores the use of the Boltzmann equation for opinion formation models. It begins with an introduction to kinetic gas theory and the Boltzmann equation, the cornerstone of the model. This is followed by opinion dynamics models in which individuals have, in addition to their opinion, a variable for leadership qualities. Political segregation is then modeled by considering spatial positions instead of assertiveness. Finally, two Monte Carlo algorithms to solve the homogeneous Boltzmann equation are introduced, enabling the simulation of one of the proposed models.
dc.format
application/pdf
dc.publisher
Universitat Politècnica de Catalunya
dc.rights
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights
Attribution-NonCommercial-ShareAlike 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject
Statistical physics
dc.subject
Stochastic processes
dc.subject
Monte Carlo method
dc.subject
Física estadística
dc.subject
Processos estocàstics
dc.subject
Simulació de Monte Carlo
dc.subject
Classificació AMS::82 Statistical mechanics, structure of matter::82C Time-dependent statistical mechanics (dynamic and nonequilibrium)
dc.subject
Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
dc.subject
Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations
dc.title
Boltzmann-type equations for opinion dynamics: Leadership and political segregation
