SEE-Rio | Palestra com Tanja Isabelle Schindler

📅 17 de setembro de 2026

O SEE-Rio recebe Tanja Isabelle Schindler, do Department of Mathematics and Statistics, University of Exeter (Reino Unido), para uma palestra especial.

Title: Diffraction, spectral and fractal analysis of (generalized) Thue--Morse measures and applications to large deviations

Abstract: The classic Thue–Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. It arises by using a diffraction algorithm of the aperiodic Thus--Morse sequence resampling diffraction one gets from physical experiments. Since it has a representation as an infinite Riesz product, many aspects of this measure have been studied in the past. Some of the difficulties emerge from the appearance of an unbounded potential in the thermodynamic formalism (a method originating from statistical mechanics, but widely used in ergodic theory).

In the generalized case, we consider Riesz products that can be regarded as diffraction measures of generalized Thue–Morse sequences, possibly over an infinite alphabet. These measures are closely related to the dynamical system arising from the doubling map together with an observable exhibiting a logarithmic singularity. For this system, we develop a generalized thermodynamic formalism beyond the standard setting, which yields explicit formulas for Birkhoff and dimension spectra.

Moreover, this new formulation of the thermodynamic formalism allows to give precise large deviation results for unbounded observables with a qualitatively different result depending if the logarithmic singularity appears at a periodic or pre-periodic non periodic point.

The talk will first give an intrduction into diffraction measures and the classical thermodynamic formalism and explains then the novelty of the results.

The talk is based on joint work with Philipp Gohlke and Marc Kesseböhmer and work in progress with Matt Nicol.

Departamento de Matemática – PUC-Rio
Sala L856
Horário: 16h

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