Grigoris Paouris

Professor, Texas A&M University

PhD, January 2004
Department of Mathematics
University of Crete

Publications

Empirical forms of the Petty projection inequality
with P. Pivovarov and K. Tatarko, Preprint.
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Can we spot a fake?
with S. Mendelson and R. Vershynin, Preprint.
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Feasibility of Circuit Polynomials without Purple Swans
with W. Deng, A. Ergur and J. M. Rojas, Proceedings of ISSAC 2024 (International Symposium on Symbolic and Algebraic Computation, July 16-19, Raleigh, NC, USA), pp. 429–436.
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Small ball probabilities for simple random tensors
with X. Hu, Preprint.
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Near-Optimal Estimation of Linear Functionals with Log-Concave Observation Errors
with S. Foucart, Inf. Inference 12 (2023), no. 4, iaad038.
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From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry
with R. Adamczak, P. Pivovarov and P. Simanjuntak, Preprint.
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Measure comparison and distance inequalities for convex bodies
with A. Koldobsky and A. Zvavitch, Indiana University Mathematics Journal 71 (2022), no. 1, 391-407.
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Hypercontractivity, and lower deviation estimates in normed spaces
with K. Tikhomirov and P. Valettas, Annals of Probability 50 (2022), no. 2, 688-734.
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Stable recovery and the coordinate small-ball behaviour of random vectors
with S. Mendelson, Geometric Aspects of Functional Analysis, 231-267, Lecture Notes in Math., 2327, Springer, Cham, 2023.
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Remarks on the Renyi entropy of a sum of iid random variables
with B. Jaye, G. Livshyts and P. Pivovarov, IEEE Transactions of Information Theory 66 (2020), 2898-2903.
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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.
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Affine isoperimetric inequalities on flag manifolds
with S. Dann and P. Pivovarov, Canadian Journal of Mathematics 77 (2025), no. 1, 252-281.
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Smoothed analysis for the condition number of structured real polynomial systems
with A. Ergur and J. M. Rojas, Mathematics of Computation 90 (2021), no. 331, 2161-2184.
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Gaussian convex bodies: a non-asymptotic approach
with P. Pivovarov and P. Valettas, Zapiski Nauchnych Seminarov POMI 457 (2017), 286-316.
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Dichotomies, structure, and concentration in normed spaces
with P. Valettas, Advances in Mathematics 332 (2018), 438-464.
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Variance estimates and almost Euclidean structure
with P. Valettas, Advances in Geometry 19 (2019), 165-189.
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On a quantitative reversal of Alexandrov's inequality
with P. Pivovarov and P. Valettas, Transactions of the American Mathematical Society 371 (2019), 3309-3324.
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A small deviation inequality for convex functions
with P. Valettas, Annals of Probability 46 (2018), 1441-1454.
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Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions
with A. Ergur and J. M. Rojas, Foundations of Computational Mathematics 19 (2019), no. 1, 131-157.
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Generalized Sudakov via Dimension Reduction - A Program
with S. Mendelson and E. Milman, Studia Mathematica 244 (2019), 159-202.
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An interpolation proof of Ehrhard’s inequality
with J. Neeman, GAFA Seminar Volume, Lecture Notes in Mathematics 2266, Vol. II (2020), 263-278.
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Randomized isoperimetric inequalities
with P. Pivovarov, Convexity and Concentration, (E. Carlen, M. Madiman, E. Werner eds.) The IMA Volumes in Mathematics and its Applications, Springer (2017), 391-425.
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An inequality for moments of log-concave functions on Gaussian random vectors
with N. Dafnis, Geometric Aspects of Functional Analysis (B. Klartag and E. Milman eds.) Lecture Notes in Mathematics 2169 (2017), 107-122.
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On Dvoretzky's theorem for subspaces of L_p
with P. Valettas, Journal of Functional Analysis 275 (2018), 2225-2252.
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Random version of Dvoretzky's theorem in l_p^n
with P. Valettas and J. Zinn, Stochastic Processes and their Applications 127 (2017), 3187-3227.
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Random ball-polyhedra and inequalities for intrinsic volumes
with P. Pivovarov, Monatshefte fur Mathematik 182 (2017), 709-729.
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On sharp bounds for marginal densities of product measures
with G. Livshyts and P. Pivovarov, Israel Journal of Mathematics 216 (2016), 877-889.
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Bounding marginal densities via affine isoperimetry
with S. Dann and P. Pivovarov, Proceedings of the London Mathematical Society 113 (2016), 140-162.
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Tropical varieties for exponential sums
with A. Ergur and J. M. Rojas, Mathematische Annalen 377 (2020), 863-882.
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Neighborhoods on the Grassmannian of marginals with bounded isotropic constant
with P. Valettas, Journal of Functional Analysis 267 (2014), 3427-3443.
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Volume of the polar of random sets and shadow systems
with D. Cordero-Erausquin, M. Fradelizi and P. Pivovarov, Mathematische Annalen 362 (2015), 1305-1325.
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Improved Holder and reverse Holder inequalities for Gaussian random vectors
with W-K. Chen and N. Dafnis, Advances in Mathematics 280 (2015), 643-689.
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A central limit theorem for projections of the cube
with P. Pivovarov and J. Zinn, Probability Theory and Related Fields 159 (2014), 701-719.
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On the singular value of random matrices
with S. Mendelson, Journal of European Mathematical Society 16 (2014), 823-834.
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Complex Intersection bodies
with A. Koldobsky and M. Zymonopoulou, Journal of the London Mathematical Society 88 (2013), 538-562.
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The isotropic position and the reverse Santalo inequality
with A. Giannopoulos and B-H. Vritsiou, Israel Journal of Mathematics 203 (2014), 1-22.
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Small ball probabilities for the volume of random convex sets
with P. Pivovarov, Discrete and Computational Geometry 49 (2013), 601-646.
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Intrinsic volumes and linear contractions
with P. Pivovarov, Proc. Amer. Math. Soc. 143 (2013), 1805-1808.
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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.
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On the approximation of a polytope by its dual L_p-centroid bodies
with E. Werner, Indiana Univ. Math. J. 62 (2013), 235-247.
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A remark on the slicing problem
with A. Giannopoulos and B-H. Vritsiou, Journal of Functional Analysis 262 (2012), 1062–1086.
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On the isotropic constant of marginals
Studia Math. 212 (2012), 219-236.
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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.
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Estimates for the affine and dual affine quermassintegrals of convex bodies
with N. Dafnis, Illinois Journal of Mathematics 56 (2012), 1005-1021.
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A probabilistic take on isoperimetric-type inequalities
with P. Pivovarov, Advances in Mathematics 230 (2012), 1402-1422.
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Isomorphic properties of intersection bodies
with A. Koldobsky and M. Zymonopoulou, Journal of Functional Analysis 261 (2011), 2697-2716.
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On the distribution of the psi(2)-norm of linear functionals on isotropic convex bodies
with A. Giannopoulos and P. Valettas, in Geometric Aspects of Functional Analysis,
Lecture Notes in Mathematics 2050 (2012), 227-253.
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Psi(a)-estimates for marginals of log-concave probability measures
with A. Giannopoulos and P. Valettas, Proceedings of the American Mathematical Society 140 (2012), 1297-1308.
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On the existence of supergaussian directions on convex bodies
Mathematika 58 (2012), 389-408.
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On the existence of subgaussian directions for log-concave measures
with A. Giannopoulos and P. Valettas, Contemporary Mathematics 545 (2011), 103-122.
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Relative entropy of cone measures and L_p centroid bodies
with E. Werner, Proc. London Math. Soc. 104 (2012), 253–286.
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Simplices in the Euclidean ball
with M. Fradelizi and C. Schutt, Canadian Math. Bulletin 55 (2012), 498-508.
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Small ball probability estimates, psi_2-behavior and the hyperplane conjecture
with N. Dafnis, Journal of Functional Analysis 258 (2010), 1933-1964.
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Small ball probability estimates for log-concave measures,
Trans. Amer. Math. Soc. 364 (2012), 287-308.
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High dimensional random sections of isotropic convex bodies
with D. Alonso-Gutierrez, J. Bastero and J. Bernues, J. Math. Anal. Appl. 361 (2010), 431–439.
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A stability result for mean width of L_p-centroid bodies
with B. Fleury and O. Guedon, Advances in Mathematics 214 (2007), 865-877.
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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.
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Concentration of mass in convex bodies
Geometric and Functional Analysis 16 (2006), 1021-1049
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Concentration of mass on isotropic convex bodies
Comptes Rendus Mathematique, 342 (2006), 179-182
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Concentration of mass on the Schatten classes
with O. Guedon, Annales de l'Institute Henri Poincare "Probabilites et Statistiques" 43 (2007), 87-99
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On the Psi_2 behavior of linear functionals on isotropic convex bodies
Studia Math. 168 (2005), 285-299
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Concentration of mass and central limit properties of isotropic convex bodies
Proc. Amer. Math. Soc. 133 (2005), 565-575.
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Quermassintegrals of a random polytope in a convex body
with M. Hartzoulaki, Arch. Math. 80 (2003), 430-438.
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Psi_2 estimates for linear functionals on zonoids
Lecture Notes in Mathematics 1807 (2003), 211-222.
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On a local version of the Aleksandrov-Fenchel inequalities for the quermassintegrals of a convex body
with A. Giannopoulos and M. Hartzoulaki, Proc. Amer. Math. Soc. 130 (2002), 2403-2412.
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On the isotropic constant of non-symmetric convex bodies
Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 1745 (2000), 239-243.
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PhD Thesis

Volume Inequalities for Sections and Projections of Convex Bodies
University of Crete, January 2004
(in Greek, pdf)

MSc Thesis

The hyperplane conjecture for convex bodies
University of Crete, April 1999
(in Greek, pdf)