40 citations · 300 across the 38 of their papers we have counts for
18 papers · 1 filter
Dimension gap and phase transition for one-dimensional random walks with reflective boundary
Maik Gröger, Johannes Jaerisch, Marc Kesseböhmer
We study - and -extensions of interval maps with at most countably many full branches modelling one-dimensional random walks without and with a reflective bou…
Generalized Thue-Morse measures: spectral and fractal analysis
Philipp Gohlke, Marc Kesseböhmer, Tanja I. Schindler
We investigate a family of Riesz products and show that they can be regarded as diffraction measures of generalized Thue-Morse sequences, possibly over an infinite alphabet. These…
Parametrized Families of Gibbs Measures and their Statistical Inference
Manfred Denker, Marc Keßeböhmer, Artur O. Lopes +1
For Hölder continuous functions , , on a subshift of finite type and we consider a parametrized family of potentials $\{F_θ= f_0+\sum_{i…
Scaling properties of the Thue--Morse measure
Michael Baake, Philipp Gohlke, Marc Kesseböhmer +1
The classic Thue--Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. Since it has a representation as an infinite Rie…
The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain
Marc Kesseböhmer, Tony Samuel, Karenina Sender
In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin b…
Minkowski measurability of infinite conformal graph directed systems and application to Apollonian packings
Marc Kesseböhmer, Sabrina Kombrink
We give conditions for the existence of the Minkowski content of limit sets stemming from infinite conformal graph directed systems. As an application we obtain Minkowski measurabi…
On the asymptotics of the -Farey transfer operator
Johannes Kautzsch, Marc Kesseböhmer, Tony Samuel +1
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic -Farey maps. We provide a family of observables which are Riemann integrable, locally…
Minkowski content and fractal Euler characteristic for conformal graph directed systems
Marc Kesseböhmer, Sabrina Kombrink
We study the (local) Minkowski content and the (local) fractal Euler characteristic of limit sets of conformal graph directed systems (cGDS) . For the local…
A Fréchet law and an Erdös-Philipp law for maximal cuspidal windings
Johannes Jaerisch, Marc Kesseböhmer, Bernd O. Stratmann
In this paper we establish a Fréchet law for maximal cuspidal windings of the geodesic flow on a Riemannian surface associated with an arbitrary finitely generated, essentially fre…
Strong renewal theorems and Lyapunov spectra for -Farey and -Lüroth systems
Marc Kesseböhmer, Sara Munday, Bernd O. Stratmann
In this paper we introduce and study the -Farey map and its associated jump transformation, the -Lüroth map, for an arbitrary countable partition of the unit interval wit…
On the Lebesgue measure of sum-level sets for continued fractions
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we give a detailed measure theoretical analysis of what we call sum-level sets for regular continued fraction expansions. The first main result is to settle a recent…
Hölder-differentiability of Gibbs distribution functions
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil's staircases) supported on limit sets…
Fractal analysis for sets of non-differentiability of Minkowski's question mark function
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we study various fractal geometric aspects of the Minkowski question mark function We show that the unit interval can be written as the union of the three sets $…
Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems
Marc Kesseböhmer, Mariusz Urbanski
We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain de…
Critical waiting time processes in infinite ergodic theory
Marc Kesseböhmer, Mehdi Slassi
We study limit laws for return time processes defined on infinite conservative ergodic measure preserving dynamical systems. Especially for the critical cases with purely atomic li…
Refined measurable rigidity and flexibility for conformal iterated function systems
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that…
Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states
Marc Kesseböhmer, Manuel Stadlbauer, Bernd O. Stratmann
We study relations between --KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator . Generalising the well--studied pur…
Limit laws for distorted return time processes for infinite measure preserving transformations
Marc Kesseböhmer, Mehdi Slassi
We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with resp…