Introduction to the Glauber dynamics for the Curie-Weiss Potts model

This thesis aims at presenting in an organized fashion the required basics to understand the Glauber dynamics as a way of simulating configurations according to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive presentation of the Curie-Weiss Potts model and its analysis. Finally, the Glauber dynamics is studied in general and applied afterwards in an exemplary way to the Curie-Weiss model as well as the Curie-Weiss Potts model. The associated considerations are supplemented with two computer simulations aiming to show the cutoff phenomenon and the temperature dependence of the convergence behavior.

Level thesis:degree_level

master

Grantor dc:publisher

Universität Potsdam

Year

2020

Author dc:creator

• Tschisgale, Paul

Contributors dc:contributor

• Zass, Alexander
• Roelly, Sylvie

• Glauber Dynamics
• Curie-Weiss Potts Model
• Mixing Times
• MCMC
• Glauber Dynamik
• Curie-Weiss Potts Modell
• Mischzeiten
• MCMC-Verfahren

Statement dc:rights

• CC-BY - Namensnennung 4.0 International

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48676

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:48676