My main research interests lie at the interface of probability theory, analysis and geometry. More precisely, I am interested in high-dimensional probability, convex geometry, the concentration of measure phenomenon, and the application of probabilistic and geometric tools to information theory.

Publications

• A note on statistical distances for discrete log-concave measures,
  (with Puja Pandey), Preprint, arXiv:2309.03197 [math.PR].
• Moments, concentration, and entropy of log-concave distributions,
  (with James Melbourne), Preprint, arXiv:2205.08293 [math.PR].
• On a conjecture of Feige for discrete log-concave distributions,
  (with Abdulmajeed Alqasem, Heshan Aravinda and James Melbourne), SIAM J. Discrete Math., Vol. 38, No. 1, pp. 93-102.
• Geometric and functional inequalities for log-concave probability sequences,
  (with James Melbourne), Discrete Comput Geom (2023). https://doi.org/10.1007/s00454-023-00528-7.
• On the equivalence of statistical distances for isotropic convex measures,
  (with Puja Pandey), Math. Inequal. Appl. 25 (2022), no. 3, 881-901.
• Concentration inequalities for ultra log-concave distributions,
  (with Heshan Aravinda and James Melbourne), Studia Math. 265 (2022), no. 1, 111-120.
• Concentration functions and entropy bounds for discrete log-concave distributions,
  (with Sergey Bobkov and James Melbourne), Combin. Probab. Comput. 31 (2022), no. 1, 54-72.
• Entropic CLT for smoothed convolutions and associated entropy bounds,
  (with Sergey Bobkov), International Mathematics Research Notices, vol. 2020, No. 21, 8057-8080, 2020.
  
• Further investigations of Rényi entropy power inequalities and an entropic characterization of s-concave densities,
  (with Jiange Li and James Melbourne), Geometric aspects of functional analysis. Vol. II, 95-123, Lecture Notes in Math., 2266, Springer, Cham, 2020.
• Local limit theorems for smoothed Bernoulli and other convolutions,
  (with Sergey Bobkov), Theory of Probability and its Applications, vol. 65, no. 1, pp. 79-102, 2020.
• Asymptotic behavior of Rényi entropy in the central limit theorem,
  (with Sergey Bobkov), High dimensional probability VIII – the Oaxaca volume, 169-200, Progr. Probab., 74, Birkhäuser/Springer, Cham, 2019.
• On the entropy power inequality for the Rényi entropy of order [0,1],
  (with James Melbourne), IEEE Transactions on Information Theory 65 (2019), no. 3, 1387-1396.
• The convexification effect of Minkowski summation,
  (with Matthieu Fradelizi, Mokshay Madiman and Artem Zvavitch), EMS Surv. Math. Sci. 5 (2018), no. 1, 1-64.
• A lower bound on the differential entropy of log-concave random vectors with applications,
  (with Victoria Kostina), Entropy 20 (2018), no. 3, Paper No. 185, 24 pp. Special Issue “Entropy and Information Inequalities”.
• A note on the convex infimum convolution inequality,
  (with Naomi Feldheim, Piotr Nayar and Jing Wang), Bernoulli 24 (2018), no. 1, 257-270.
• Variants of the entropy power inequality,
  (with Sergey Bobkov), IEEE Transactions on Information Theory 63 (2017), no. 12, 7747-7752.
• On the stability of Brunn-Minkowski type inequalities,
  (with Andrea Colesanti and Galyna Livshyts), J. Funct. Anal. 273 (2017), no. 3, 1120-1139.
• On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities,
  (with Galyna Livshyts, Piotr Nayar and Artem Zvavitch), Trans. Amer. Math. Soc. 369 (2017), no. 12, 8725-8742.
• Borell’s generalized Prékopa-Leindler inequality: A simple proof,
  J. Convex Anal. 24 (2017), no. 3, 807-817.
• Do Minkowski averages get progressively more convex?,
  (with Matthieu Fradelizi, Mokshay Madiman and Artem Zvavitch), C. R. Math. Acad. Sci. Paris 354 (2016), no. 2, 185-189.
• On the improvement of concavity of convex measures,
  Proc. Amer. Math. Soc. 144 (2016), no. 2, 775-786.
• Concavity properties of extensions of the parallel volume,
  Mathematika 62 (2016), no. 1, 266-282.
• A note on an Lp-Brunn-Minkowski inequality for convex measures in the unconditional case,
  Pacific J. Math. 277 (2015), no. 1, 187-200.
• On the analogue of the concavity of entropy power in the Brunn-Minkowski theory,
  (with Matthieu Fradelizi), Advances in Applied Mathematics 57 (2014), 1-20.

Conference Papers

• Rényi entropy power inequalities for s-concave densities,
  (with Jiange Li and James Melbourne), Proceedings 2019 IEEE International Symposium on Information Theory, Paris, France, July 2019.
• Entropic central limit theorem for Rényi entropy,
  (with Jiange Li and James Melbourne), Proceedings 2019 IEEE International Symposium on Information Theory, Paris, France, July 2019.
• New connections between the entropy power inequality and geometric inequalities,
  (with Victoria Kostina), Proceedings 2018 IEEE International Symposium on Information Theory, Vail, Colorado, June 2018.
• A Rényi entropy power inequality for log-concave vectors and parameters in [0,1],
  (with James Melbourne), Proceedings 2018 IEEE International Symposium on Information Theory, Vail, Colorado, June 2018.
• A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory,
  (with Victoria Kostina), Proceedings 2017 IEEE International Symposium on Information Theory, Aachen, Germany, June 2017.

Thesis

• Geometry of Convex Measures and Links with Information Theory,
  Ph.D. in Mathematics
• Inégalités de grandes déviations dans les corps convexes inconditionnels
  (Large deviation inequalities in unconditional convex bodies),
  Master Mathematics and Applications