Ariel Rapaport's Home page
I am a Senior Lecturer in the Department of Mathematics at the Technion, Haifa.
My research focuses on fractal geometry and ergodic theory, particularly on the dimension theory of stationary fractal measures.
I am the recipient of an ERC Starting Grant (“DIM-FRACTAL” 2026–2031).
Students and postdoctoral researchers interested in joining the project are welcome to get in touch.
E-mail: arapaport [at] technion [dot] ac [dot] il
Dimension of Furstenberg measures on CP^1, preprint, 2025. (with Haojie Ren)
Dimension of self-conformal measures associated to an exponentially separated analytic IFS on R, preprint, 2024.
Dimension of Bernoulli Convolutions in R^d, to appear in Annals of Probability. (with Haojie Ren)
Dimension of diagonal self-affine sets and measures via non-conformal partitions, to appear in Proceedings of the LMS.
On self-affine measures associated to strongly irreducible and proximal systems, Advances in Mathematics, 449 (2024).
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, Duke Math. J., 173.3 (2024), 513-602. (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)