Piotr Nayar
Assistant Professor
University of Warsaw, Institute of Mathematics
Faculty of Mathematics, Informatics and Mechanics
Publications
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A. Eskenazis, P. Nayar, T. Tkocz, Resilience of cube slicing in l_p, to appear in Duke Math. J.
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A. Eskenazis, P. Nayar, T. Tkocz, Distributional stability of the Szarek and Ball inequalities, Math. Ann. (2023), doi: 10.1007/s00208-023-02669-9
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M. Białobrzeski, P. Nayar, Renyi entropy and variance comparison for symmetric log-concave random variables, IEEE Trans. Inform. Theory, doi: 10.1109/TIT.2023.3243956.
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G. Chasapis, P. Nayar, T. Tkocz, Slicing ℓp-balls reloaded: stability, planar sections in ℓ1, Annals of Probability, 50, no. 6, 2022, 2344-2372.
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A. Havrilla, P. Nayar, T. Tkocz, Khinchin-type inequalities via Hadamard’s factorisation,
Int. Math. Res.
Not., Vol. 2023 (3), 2023, 2429–2445.
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M. Bartczak, P. Nayar and S. Zwara, Sharp Variance-Entropy Comparison for Nonnegative Gaussian Quadratic
Forms, IEEE Trans. Inform. Theory, vol. 67, no. 12, 2021, 7740-7751.
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G. Morina, K. Latuszynski, P. Nayar, A. Wendland, From the Bernoulli Factory to a Dice Enterprise via Perfect Sampling of Markov Chains, Annals of Applied Probability 32 (2022), no. 1, 327–359.
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I. Chlebicka, P. Nayar, Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem,
Math. Meth. Appl. Sci. 2021, 1–25.
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R. Latała, P. Nayar,
Hadamard products and moments of random vectors, Adv. Math. 375 (2020), 107414, arXiv:1907.09812
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M. Madiman, P. Nayar, T. Tkocz, Sharp moment-entropy inequalities and capacity bounds for log-concave distributions,
IEEE Transactions on Information Theory 67 (1) 2021, 81-94, arXiv:1811.00345
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M. Madiman, P. Nayar, T. Tkocz, Two remarks on generalized entropy power inequalities,
Israel Seminar (GAFA) 2017-2019 Volume II, Lecture Notes in Mathematics, vol 2266, arXiv:1904.02314
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P. Nayar, T. Tkocz, On a convexity property of sections of the cross-polytope, 2018, Proc. Amer.
Math. Soc. 148 (3), 2020, 1271-1278, arXiv:1810.02038
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A. Bonami, R. Latała, P. Nayar, T. Tkocz, Bounds on moments of weighted sums of finite Riesz products,
Journal of Fourier Analysis and Applications, 26 (2), Article number: 84 (2020), arXiv:1805.10918
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A. Eskenazis, P. Nayar, T. Tkocz, Sharp comparison of moments and the log-concave moment problem,
Advances in Mathematics, Vol. 334, 2018, 389-416.
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A. Eskenazis, P. Nayar, T. Tkocz, Gaussian mixture: entropy and geometric inequalities, 2016, Annals of
Probability, Vol. 46 (5), 2018, 2908-2945.
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P. Nayar, T. Tkocz, A multidimensional analogue of the Rademacher-Gaussian tail comparison, Proc. Amer.
Math. Soc., Vol. 146 (1), 2018, 413-419.
- K. Ball, P. Nayar, T. Tkocz, A reverse entropy power inequality for log-concave random vectors, Studia
Mathematica 235, 2016, 17-30.
- N. Feldheim, A. Marsiglietti, P. Nayar, J. Wang, A note on the convex infimum convolution inequality, Bernoulli, Vol. 24 (1), 2018, 257–270.
- S. Bobkov, P. Nayar, P. Tetali, Concentration Properties of Restricted Measures with
Applications to Non-Lipschitz Functions, GAFA, Lecture Notes in Mathematics, Vol. 2169/2017, 25-53.
- G. Livshyts, A. Marsiglietti, P. Nayar, A. Zvavitch, On the Brunn-Minkowski inequality for general measures
with applications to new isoperimetric type-inequalities, Trans. Amer. Math. Soc., Vol. 369 (12), 2017, 8725–8742.
- M. Korzec, P. Nayar, P. Rybka, Global attractors of sixth order PDEs describing the faceting of growing surfaces, Journal of Dynamics and Differential Equations, Vol. 28 (1), 2016, 49-67
- E. Damek, R. Latała, P. Nayar, T. Tkocz, Two-sided bounds for L_p-norms of combinations of products of independent random variables, Stochastic Processes and their Applications Vol. 125(4), 2015, 1688-1713.
- O. Guedon, P. Nayar, D. Ryabogin, T. Tkocz, A. Zvavitch, Analytical and probabilistic methods in the
geometry of convex bodies, IMPAN Lecture Notes 2, 2014, ISBN 978-83-86806-24-9
- Nayar P., Pilat B., A note on the rational cuspidal curves, Bull. Polish Acad. Sci. Math. Vol. 62, 2014, 117-123.
- Nayar P., FKN theorem on the biased cube, Colloq. Math. Vol. 137, 2014, 253-261.
- Nayar P., Tkocz T., A note on certain convolution operators, GAFA (Israel Seminar 2011--2013 Vol. 2116/2014, Chapter 26), Klartag B., Milman E., Springer: 405-412.
- P.Nayar, T. Tkocz, S-inequality for certain product measures, Math. Nachr. 287 (2014), No. 4, 398-404.
- P. Nayar, T. Tkocz, The unconditional case of the complex S-inequality, Israel J. Math. 197 (2013), no. 1, 99-106.
- P. Nayar, T. Tkocz, A Note on a Brunn-Minkowski Inequality for the Gaussian Measure, Proc. Amer. Math. Soc. 141 (2013), no. 11, 4027-4030.
- P. Nayar, T. Tkocz, On a
Loomis-Whitney type inequality for permutationally invariant unconditional
convex bodies, GAFA, Lecture Notes in
Mathematics, Vol.
2050/2012, 327-333.
- P. Nayar P, K. Oleszkiewicz,
Khinchine type inequalities with optimal constants via ultra log-concavity,
Positivity Vol. 16, 2012, 359-371.
- P. Nayar, M. Korzec, P. Rybka, Global weak
solutions to a sixth order Cahn-Hilliard type equation, SIAM
J. Math. Anal., 44(5), 3369-3387.
- P. Nayar, On Polynomially Bounded
Harmonic Functions on the Z^d Lattice, Bull. Polish Acad. Sci. Math.
57 (2009), 231-242.