Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 771-785

SELF-AFFINE SETS WITH NON-COMPACTLY SUPPORTED RANDOM PERTURBATIONS

Thomas Jordan and Natalia Jurga

The University of Bristol, School of Mathematics
University Walk, Clifton, Bristol, BS8 1TW, UK; thomas.jordan 'at' bristol.ac.uk

The University of Bristol, School of Mathematics
University Walk, Clifton, Bristol, BS8 1TW, UK; nj0529 'at' bristol.ac.uk

Abstract. 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.

2010 Mathematics Subject Classification: Primary 28A78, 28A80.

Key words: self-affine sets, Hausdorff dimension, random perturbations.

Reference to this article: T. Jordan and N. Jurga: Self-affine sets with non-compactly supported random perturbations. Ann. Acad. Sci. Fenn. Math. 39 (2014), 771-785.

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doi:10.5186/aasfm.2014.3948