Research
Publications and preprints
- Transient random walks on the space of lattices, with A. Péneau.
to appear in Geom. Funct. Anal. (2026), arXiv - Projections of self-affine fractals, with I.D. Morris.
Invent. Math. (2026), arXiv --- [slides], [video] - Joint translation spectrum and Manhattan manifolds, with S. Cantrell and E. Reyes
(being comprehensively rewritten/extended - New title: Translation cones, growth indicators, and Manhattan manifolds for hyperbolic groups) arXiv (2024, old version) - Stationary probability measures on projective spaces 2: The critical case, with R. Aoun.
Duke Math. J. (2025), arXiv --- [video] - A variational principle relating self-affine measures to self-affine sets, with I.D. Morris.
(submitted) arXiv (2023) - Stationary measures for SL(2,R)-actions on homogeneous bundles over flag varieties, with A. Gorodnik and J. Li.
J. Reine Angew. Math. (2024), arXiv - Stationary probability measures on projective spaces 1: Block-Lyapunov dominated systems, with R. Aoun.
Math. Ann. (2024), arXiv - Counting and boundary limit theorems for representations of Gromov-hyperbolic groups, with S. Cantrell.
Proc. London Math. Soc. (2023), arXiv --- [slides] - Random walks on hyperbolic spaces: second order expansion of the rate function at the drift, with R. Aoun and P. Mathieu.
Journal de l'Ecole Polytechnique. (2023), arXiv - Expanding measures: Random walks and rigidity on homogeneous spaces, with R. Prohaska and R. Shi.
Forum of Math, Sigma. (2023), arXiv --- [slides] , [video] - Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative, with R. Aoun.
Probab. Theory and Rel. Fields. (2022), arXiv --- [slides] , [video] - Large deviations for random walks on Gromov-hyperbolic spaces, with A. Boulanger, P. Mathieu and A. Sisto.
Annales Scientifiques de l'Ecole Normale Supérieure. (2023), arXiv --- [slides] , [video] - (Non)-escape of mass and equidistribution for horospherical actions on trees, with C. Ciobotaru and V. Finkelshtein.
Mathematische Zeitschrift. (2021), arXiv --- [slides] , [video] - A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures, with I.D. Morris.
JEMS. (2023), arXiv --- [slides] , [video] - Law of large numbers for the spectral radius of random matrix products, with R. Aoun.
American J. of Math. (2021), arXiv - Markov random walks on homogeneous spaces and Diophantine approximation on fractals, with R. Prohaska.
Transactions of American Math. Soc. (2020), arXiv - A strongly irreducible affine iterated function system with two invariant measures of maximal dimension, with I. D. Morris.
Erg. Theory and Dyn. Syst. (2021), arXiv - Measure rigidity for horospherical subgroups of groups acting on trees, with C. Ciobotaru and V. Finkelshtein.
International Math. Resarch Notices. (2021), arXiv --- [slides] , [video] - The joint spectrum (I), with E. Breuillard.
Journal of London Math. Soc. (2021), arXiv --- [Carlos Matheus' blog post] - Large deviation principle for random matrix products.
Annals of Probability. (2019), arXiv --- (See also announcement in CRAS (2017)). - Doctoral Thesis
Other publications
- Pressure metrics
Arbeitsgemeinschaft: Higher Rank Teichmüller Theory, Oberwolfach Report 47/2022. - Bourgain–Gamburd machine
Arbeitsgemeinschaft: Thin Groups and Super-approximation, Oberwolfach Report 50/2021. - Ledrappier–Young Rigidity
Arbeitsgemeinschaft: Zimmer’s Conjecture, Oberwolfach Report 48/2019.
Work in progress
- Counting limit theorems for Anosov representations. (with S. Cantrell, I. Cipriano and R. Dougall)
- Projections and sumsets of self-affine fractals 2-3. (with I.D. Morris)
- Finiteness properties for joint spectral radii in SL(2,R). (with E. Breuillard)
- Ergodic optimization for a class of skew-product systems. (with J. Bochi)
- Expanding affine random walks. (with A. Péneau)
- Growth indicator for semisimple linear groups.