The space of harmonic functions for transfer operators and phase transitions

Date. October 02, 14h00m (UTC/GMT+1)

Speaker.  Leandro Cioletti (Universidade de Brasília)

Title. The space of harmonic functions for transfer operators and phase transitions


It was recently proved that the set of DLR-Gibbs measures, associated with a uniformly absolutely summable interaction on the lattice N, coincides with the set of P(f)-conformal measures associated with a suitable continuous potential f. In this talk, we explore this result and prove a new relation between the set of extreme P(f)-conformal measures and the dimension of the Perron-Frobenius eigenspace of the L1-extension of the transfer operator associated with the potential f. In particular, we show that such eigenspace's geometric multiplicity can only be greater than one when a first-order phase transition occurs. We obtain this result by looking at the transfer operator's extension as a Markov Process in the Hopf's sense. Applications for equilibrium states associated with low regular potentials will be discussed, and an interesting example, where the space of harmonic functions has dimension two, will be presented. We will finish with a discussion on the Functional Central Limit Theorem for equilibrium states and non-local observables, which holds for observables in the Banach space of generalized Hölder continuous functions, where the transfer operator acts without the spectral gap property.


Online Zoom meeting (Session will open some minutes before 14h00)

Meeting ID: 928 5638 8700

Password: 495304

Date and Venue

Start Date
Online seminar


Leandro Cioletti

Speaker's Institution

Universidade de Brasília


Dynamical Systems