arXiv subjects

Natalia Jurga

Publications and source records attributed to Natalia Jurga.

21 records · Page 2Linked to original sources

arXiv2018

A new proof of the dimension gap for the Gauss map

Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map $T(x)= \frac{1}{x} \mod 1$ satisfy a `dimension gap' meaning that for some $c>0$, $\sup_{\mathbf{p}} \dim μ_{\mathbf{p}} <1-c$, where $μ_{\mathbf{p}}$ denotes the (pushforward) Bernoulli measure for the countable probability vector $\mathbf{p}$. In this paper we propose a new proof of the dimension gap. By using tools from thermodynamic formalism we show that the problem reduces to obtaining uniform lower bounds on the asymptotic variance of a class of potentials.

math.DS↗

arXiv2018

Maximising Bernoulli measures and dimension gaps for countable branched systems

Kifer, Peres, and Weiss proved that there exists $c_0>0,$ such that $\dim μ\leq 1-c_0$ for any probability measure $μ$ which makes the digits of the continued fraction expansion i.i.d. random variables. In this paper we prove that amongst this class of measures, there exists one whose dimension is maximal. Our results also apply in the more general setting of countable branched systems.

math.DS↗

arXiv2014

Self-affine sets with non-compactly supported random perturbations

In this note we consider the Hausdorff dimension of self-affine sets with random perturbations. We extend previous work in this area by allowing the random perturbation to be distributed according to distributions with unbounded support as long as the measure of the tails of the distribution decay super polynomially.

math.DS↗