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About ising and potts models on cayley trees and bayesian networks

Cohen Tervaert, Gerard (2019) About ising and potts models on cayley trees and bayesian networks. Master's Thesis / Essay, Mathematics.

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Abstract

We perform numerical estimates for the q-state Potts model on a k-order Cayley tree. Külske, Rozikov and Khakimov explicitly calculated up to 2^q − 1 TISGMs (Translation Invariant Splitting Gibbs Measures) for the binary tree (k = 2), without an external field (α = 0). We extend these results numerically for k > 2 and α ≠ 0. We conjecture that for α ≥ k − 1 the model has niqueness. Additionally, decay of memory is proved for a Potts-type model on a Bayesian network with up to two parents and a counterexample is given for a more general case.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor:
Supervisor nameSupervisor E mail
Enter, A.C.D. vanA.C.D.van.Enter@rug.nl
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 12 Mar 2019
Last Modified: 13 Mar 2019 08:46
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/19261

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