One-sided versus two-sided aspects in Dyson models

Speaker(s)

Aernout van Enter

Affiliation

University of Groningen

Language of the talk

English

Date

Oct. 23, 2025, 4:15 p.m.

Room

room 5070

Seminar

Seminar "Mathematics and Physics of Complex Systems"

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We discuss a number of recent results about  Dyson models, which are ferromagnets with polynomially decaying interactions. We show that at low temperatures their Gibbs measures (which have continuous two-sided conditional probabilities) are not g-measures as they don't have one-sided conditional probabilities. Moreover we compare half-line and whole-line Gibbs measures. We show that at low temperatures random boundary conditions give rise to  metastates living on mixed states, and that at high temperatures Transfer Operator eigenfunctions are continuous when the decay parameter is larger than 3/2, for closely related reasons.

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