Research

Papers/Preprints

Empirical forms of the Petty projection inequality, with P. Pivovarov, K. Tatarko, preprint, ArXiv 

Can we spot a fake?, with S. Mendelson and R. Vershynin, preprint, ArXiv 

Feasibility of Circuit Polynomials without Purple Swans, with Weixun Deng, Alperen Ergur, and J. Maurice Rojas), in Proceedings of ISSAC 2024 (International Symposium on Symbolic and Algebraic Computation, July 16-19, Raleigh, NC, USA), pp. 429–436.

From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry, with R. Adamczak, P. Pivovarov and Paul Simanjuntak. to appear in JEMS. ArXiv

Affine isoperimetric inequalities on flag manifolds, with S. Dann and P. Pivovarov, to appear in Proc. Can.Math.Soc. ArXiv

Stable recovery and the coordinate small-ball behavior of random vectors, with S. Mendelson.  GAFA Seminar Notes. Lecture Notes in Math., 2327, Springer, Cham, 2023, 231–267. ArXiv

Near-Optimal Estimation of Linear Functionals with Log-Concave Observation Errors, with S. Foucart, Inf. Inference 12 (2023), no. 4, iaad038. ArXiv

Measure comparison and distance inequalities for convex bodies, with A. Koldobsky and A. Zvavitch. Indiana Univ. Math. J. 71 (2022), no. 1, 391–407 . Arxiv

Hypercontractivity and lower deviation estimates in norms spaces, with K, Tikhomirov and P. Valettas, Ann. Probab. 50 (2022), no. 2, 688–734. ArXiv

Non-asymptotic results for singular values of Gaussian matrix products., with Boris Hanin, Geom. Funct. Anal. 31 (2021), no. 2, 268–324. Arxiv

Smoothed analysis for the condition number of structured real polynomial systems, with A. Ergur and M. Rojas, Math. Comp. 90 (2021), no. 331, 2161–2184. ArXiv

Remarks on the Renyi Entropy of a sum of IID random variables, with B. Jaye, G. Livshyts, P. Pivovarov. IEEE Trans. Inform. Theory 66 (2020), no. 5, 2898–2903. ArXiv

Tropical Varieties for Exponential Sums and their Distance to Amoebae, with A. Ergur and M. Rojas, Math. Ann. 377 (2020), no. 3-4, 863–882. , ArXiv.

A Faster Solution to Smale’s 17th Problem I: Real Binomial Systems, with K. Phillipson and J. M. Rojas. ISSAC’19, Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation, [323--330], ACM, New York, 2019. ArXiv

On a quantitative reversal of Alexandrov’s inequality, with P. Pivovarov and P. Valettas, Trans. Amer. Math. Soc. 371 (2019), no. 5, 3309–3324. ArXiv

Generalized dual Sudakov minoration via dimension-reduction–a program, with S. Mendelson and E. Milman, Studia Math. 244 (2019), no. 2, 159–202. ArXiv

Variance estimates and almost Euclidean structure, with P. Valettas, Adv. Geom. 19 (2019), no 2, 165–189. ArXiv

Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions, with A. Ergur and M. Rojas, Found. Comput. Math. 19 (2019), no. 1, 131–157. ArXiv

Dichotomies, structure, and concentration in normed spaces, with P. Valettas, Adv. Math. 332 (2018), 438–464. ArXiv

A Gaussian small deviation inequality for convex functions, with P. Valettas, Ann. Probab. 46 (2018), no. 3, 1441–1454. ArXiv

On Dvoretzky’s theorem for subspaces of Lp, with P. Valettas, J. Funct. Anal. 275 (2018), (8), 2225–2252. ArXiv

Gaussian convex bodies: a non-asymptotic approach, with P. Pivovarov and P. Valettas, Zapiski Nauchnych Seminarov POMI 457 (2017), 286–316.  

An interpolation proof of Ehrhard’s inequality, with J. Neeman, Geometric aspects of functional analysis. Vol. II, 263–278, Lecture Notes in Math., 2266, Springer. ArXiv

Randomized Isoperimetric Inequalities, with P. Pivovarov, Convexity and concentration, 391–425, IMA Vol. Math. Appl., 161, Springer, New York, 2017. ArXiv

An inequality for moments of log-concave functions on Gaussian random vectors, with N. Dafnis, GAFA seminar notes, 107–122, Lecture Notes in Math.,2169, Springer, Cham, 2017. ArXiv

Random ball-polyhedra and inequalities for intrinsic volumes, with P. Pivovarov, Monatsh. Math. 182 (2017), 709–729. ArXiv

Random version of Dvoretzky’s theorem in l_p , with P. Valettas and J. Zinn. Stochastic Process. Appl. 127 (2017), no 10, 3187–3227. ArXiv

On sharp bounds for marginal densities of product measures, with G. Livshyts and P. Pivovarov, Israel J. Math. 216 (2016), 877–889. ArXiv

Bounding marginal densities via affine isoperimetry, with S. Dann and P. Pivovarov, Proc. Lond. Math. Soc. 113 (2016), 140–162. ArXiv

Improved Holder and reverse Holder inequalities for Gaussian random vectors, with W-K. Chen and N. Dafnis, Adv. Math. 280 (2015), 643–689. ArXiv

Shadow systems and the volume of the polar of random sets, with D. Cordero- Erausquin, M. Fradelizi and P. Pivovarov, Math. Ann. 362 (2015), no 3-4, 1305–1325. ArXiv

Neighborhoods on the Grassmannian of marginals with bounded isotropic constant, with P. Valettas, J. Funct. Anal. 267 (2014), no 9, 3427–3443. ArXiv

A central limit theorem for projections of the cube, with P. Pivovarov and J. Zinn, Probab. Theory Related Fields 159 (2014), No 3-4, 701–719. ArXiv

The isotropic position and the reverse Santalo inequality, with A. Giannopoulos and B-H. Vritsiou, Israel J. Math. 203 (2014), no 1, 1–22. ArXiv

On the singular value of random matrices, with S. Mendelson, J. Eur. Math. Soc. (JEMS) 16 (2014), no 4, 823-834. 

Small ball probabilities for the volume of random convex sets, with P. Pivovarov, Discrete Comput. Geom. 49 (2013), no. 3, 601–646. 

Complex Intersection Bodies, with A. Koldobsky and M. Zymonopoulou, Journal of the London Mathematical Society (2) 88 (2013), no 2, 538–562. ArXiv

Intrinsic volumes and linear contractions, with P. Pivovarov, Proc. Amer. Math. Soc. 141 (2013), no. 5, 1805–1808. 

On the approximation of a polytope by its dual Lp-centroid bodies, with E. Werner, Indiana Univ. Math. J. 62 (2013), no 1, 235–248. ArXiv

On generic chaining and the smallest singular value of random matrices with heavy tails, with S. Mendelson, Journal of Functional Analysis 262 (2012), 3775-3811. ArXiv

A remark on the slicing problem, with A. Giannopoulos and B-H. Vritsiou,Journal of Functional Analysis 262 (2012), 1062–1086. ArXiv

On the isotropic constant of marginals, Studia Math. 212 (2012), 219–236. 

Comparing the M-position with some classical positions of convex bodies, with E. Markessinis and Ch. Saroglou, Math. Proc. Cambridge Philos. Soc. 152 (2012), 131–152.

Estimates for the affine and dual affine quermassintegrals of convex bodies, with N. Dafnis, Illinois Journal of Mathematics 56 (2012), no 4, 1005–1021.

On the distribution of the ψ2-norm of linear functionals on isotropic convex bodies, with A. Giannopoulos and P. Valettas, Lecture Notes in Mathematics, 2050 (2012) 227–253.

A probabilistic take on isoperimetric inequalities, with P. Pivovarov, Advances in Mathematics, 230, (2012), 1402–1422.

Ψα-estimates for marginals of log-concave probability measures, with A. Giannopoulos and P. Valettas. Proceedings of the American Mathematical Society 140 (2012), 1297–1308.

On the existence of supergaussian directions on convex bodies. Mathematika, 58, 389–408.

Simplices in the Euclidean ball, with M. Fradelizi and C. Schutt. Canad. Math. Bull. (55), (2012) 498–508.

Small ball probability estimates for log-concave measures. Trans. Amer. Math. Soc. 364 (2012), 287–308.

Isomorphic properties of intersection bodies, with A. Koldobsky and M. Zymonopoulou, Journal of Functional Analysis, 261 (2011) 2697–2716.ArXiv

On the existence of subgaussian directions for log-concave measures, with A. Giannopoulos and P. Valettas. Contemporary Mathematics 545 (2011), 103–122.

Relative entropy of cone measures and Lp centroid bodies , with E. Werner. Proc. London Math Soc. (2011). ArXiv

Small ball probability estimates, ψ2-behavior and the hyperplane conjecture, with N. Dafnis, Journal of Functional Analysis 258 (2010), 1933–1964

High dimensional random sections of isotropic convex bodies, with D. Al- sonso, J. Bastero and J. Bernu ́es. Journal of Mathematical Analysis and Applications, 361, (2010), 431–439.

A stability result for mean width of Lp -centroid bodies, with B. Fleury and O. Gu ́edon, Advances in Mathematics, 214 (2007) 865-877.

A note on subgaussian estimates for linear functionals on convex bodies, with A. Giannopoulos and A. Pajor, Proc. Amer. Math. Soc. 135 (2007), 2599- 2606. ArXiv

Concentration of mass on the Schatten classes, with O. Gu ́edon, Ann. I. H. Poincar ́e - PR 43 (2007), 87-99.

Concentration of mass in convex bodies, Geom. Funct. Anal. Vol. 16 (2006) 1021-1049.

Concentration of mass on isotropic convex bodies , Comptes Rendus Mathematique, 342 (2006), 179-182.

Concentration of mass and central limit properties of isotropic convex bodies, Proc. Amer. Math. Soc. 133 (2005), 565-575.

On the ψ2-behavior of linear functionals on isotropic convex bodies, Studia Math. 168 (2005), 285-299.

Quermassintegrals of a random polytope in a convex body, with M. Hart- zoulaki, Arch. Math. 80 (2003), 430-438.

Ψ2-estimates for linear functionals on zonoids, Geometric Aspects of Functional Analysis (Milman-Schechtman eds.), Lecture Notes in Mathematics 1807, Springer, Berlin (2003), 211-222.

On a local version of the Aleksandrov-Fenchel inequality for the quermassintegrals of a convex body, with A. Giannopoulos and M. Hartzoulaki, Proc. Amer. Math. Soc. 130 (2002), 2403-2412.

On the isotropic constant of non-symmetric convex bodies, Geometric Aspects of Functional Analysis (Milman-Schechtman eds.), Lecture Notes in Mathematics 1745, Springer, Berlin (2000), 238-243 .