Gibbs measures for models on lines and trees

Endo, E. O., 2018, [Groningen]: Rijksuniversiteit Groningen. 106 p.

Research output: ThesisThesis fully internal (DIV)Academic

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  • Eric Ossami Endo
The thesis consists of a number of results.
1) We show that the Gibbs measures of the Dyson model at sufficiently low temperature are not g-measures.

2) We add a spatially dependent inhomogeneous external field to the ferromagnetic Ising model on a Cayley tree, and we show the phase diagram depending on the decay of the external field.

3) We count and estimate the number of contours on a family of trees, show a characterization of trees that has infinite number of contours of a fixed size, and we compare with the other definitions of contours, such as Peierls contours and Rozikov contours.

4) We show the local limit behavior of the spatial Gibbs random graphs defined in the paper of Mourrat and Valesin, Spatial Gibbs random graphs.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Bissacot, R. , Supervisor, External person
  • van Enter, A C D, Supervisor
  • Rodrigues Valesin, Daniel, Co-supervisor
  • Fontes, L.R., Assessment committee, External person
  • Kuelske, C., Assessment committee, External person
  • Mueller, T, Assessment committee, External person
  • Verbitskiy, Evgeny, Assessment committee
Award date29-Jun-2018
Place of Publication[Groningen]
Print ISBNs978-94-034-0793-7
Electronic ISBNs978-94-034-0792-0
Publication statusPublished - 2018

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