I am a senior lecturer at the Department of Mathematics at the Technion.
My research interests are Fractal geometry and Ergodic theory.
Postdoc and student positions may be available. Contact me for more details.
E-mail: arapaport [at] technion [dot] ac [dot] il
Publications and preprints
Dimension of diagonal self-affine sets and measures via non-conformal partitions, preprint, 2023.
On self-affine measures associated to strongly irreducible and proximal systems, preprint, 2022.
On the Rajchman property for self-similar measures on R^d, Advances in Mathematics, 403 (2022).
Self-similar measures associated to a homogeneous system of three maps, to appear in Duke Math. J. (with Péter Varjú)
Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure, Transactions of the AMS, 374 (2021), 5225-5268.
Proof of the exact overlaps conjecture for systems with algebraic contractions, Annales Scientifique de l'ENS, 55 (2022), 1357–1377.
Dimension of ergodic measures projected onto self-similar sets with overlaps, Proceedings of the LMS, 122.2 (2021), 191-206. (with Thomas Jordan)
Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps, Journal of the EMS, 24 (2022), 2361-2441. (with Mike Hochman)
On self-similar measures with absolutely continuous projections and dimension conservation in each direction, Ergodic Theory and Dynamical Systems, 40 (2020), 3438-3456.
Geometric Law for Multiple Returns until a Hazard, Nonlinearity, 32.4 (2019), 1525-1545. (with Yuri Kifer)
Hausdorff dimension of planar self-affine sets and measures, Inventiones mathematicae, 216 (2019), 601-659. (with Balázs Bárány and Mike Hochman)
A self-similar measure with dense rotations, singular projections and discrete slices, Advances in Mathematics, 321 (2017), 529-546.
A dimension gap for continued fractions with independent digits - the non stationary case, Israel Journal of Mathematics, 227.2 (2018), 911-930.
On self-affine measures with equal Hausdorff and Lyapunov dimensions, Transactions of the AMS, 370 (2018), 4759-4783.
On the Hausdorff and packing measures of slices of dynamically defined sets, Journal of Fractal Geometry, 3 (2016), 33-74.
Compound Poisson statistics for multiple returns in shrinking cylinders for mixing processes, Ergodic Theory and Dynamical Systems, 36 (2016), 1616-1643.
Poisson and compound Poisson approximations in conventional and nonconventional setups, Probability Theory and Related Fields, 160 (2014), 797-831. (with Yuri Kifer)