I am a Herchel Smith Postdoctoral Research Fellow in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.
My research interests are Fractal geometry and Ergodic theory.
E-mail: ariel.rapaport [at] mail [dot] huji [dot] ac [dot] il
Publications and preprints
- Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure, preprint, 2020.
- Proof of the exact overlaps conjecture for systems with algebraic contractions, preprint, 2020.
- Dimension of ergodic measures projected onto self-similar sets with overlaps, To appear in Proceedings of the LMS. (with Thomas Jordan)
- Hausdorff Dimension of Planar Self-Affine Sets and Measures with Overlaps, preprint, 2019. (with Mike Hochman)
- On self-similar measures with absolutely continuous projections and dimension conservation in each direction, To appear in Ergodic Theory and Dynamical Systems.
- 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 Balazs Barany 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)