Tomasz Adrian Krzysztof Tkocz

Mathematics

Publications and preprints


  • J. Melbourne, T. Tkocz, K. Wyczesany,
    A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies,
    submitted. [pdf]

  • S. Myroshnychenko, C. Tang, K. Tatarko, T. Tkocz,
    Stability of simplex slicing and Lipschitzness of sections,
    submitted. [pdf]

  • J. Kalarickal, D. Rotunno, S. Singh, T. Tkocz,
    Convexity properties of sections of 1-symmetric bodies and Rademacher sums,
    submitted. [pdf]

  • X. He, T. Tkocz, K. Wyczesany,
    A sharp Gaussian tail bound for sums of uniforms,
    to appear in Israel J. Math. [pdf]

  • N. Glover, T. Tkocz, K. Wyczesany,
    Stability of polydisc slicing,
    Mathematika 69 (2023), no. 4, 1165-1182. [pdf]

  • A. Eskenazis, P. Nayar, T. Tkocz,
    Distributional stability of the Szarek and Ball inequalities,
    to appear in Math. Ann. [pdf]

  • A. Eskenazis, P. Nayar, T. Tkocz,
    Resilience of cube slicing in ℓp,
    to appear in Duke Math. J. [pdf]

  • P. Nayar, T. Tkocz,
    Extremal sections and projections of certain convex bodies: a survey,
    343-390, Adv. Anal. Geom., 9, De Gruyter, Berlin, 2023. [pdf]

  • J. Jenkins, T. Tkocz,
    Complex Hanner's inequality for many functions,
    to appear in Israel J. Math. [pdf]

  • G. Chasapis, S. Singh, T. Tkocz,
    Haagerup’s phase transition at polydisc slicing,
    to appear in Anal. PDE. [pdf]

  • G. Chasapis, A. Eskenazis, T. Tkocz,
    Sharp Rosenthal-type inequalities for mixtures and log-concave variables,
    Bull. Lond. Math. Soc. 55 (2023), no. 3, 1222–1239. [pdf]

  • Y. Cheng, Y. Liu, T. Tkocz, A. Xu,
    Typical values of extremal-weight combinatorial structures with independent symmetric weights,
    Electron. J. Combin. 30 (2023), no. 1, Paper No. 1.12, 12 pp. [pdf]

  • J. Li, T. Tkocz,
    Tail bounds for sums of independent two-sided exponential random variables,
    High dimensional probability IX—the ethereal volume, 143–154, Progr. Probab., 80, Birkhäuser/Springer, Cham, 2023. [pdf]

  • G. Chasapis, S. Singh, T. Tkocz,
    Entropies of sums of independent gamma random variables,
    J. Theoret. Probab. 36 (2023), no. 2, 1227–1242. [pdf]

  • G. Chasapis, P. Nayar, T. Tkocz,
    Slicing ℓp-balls reloaded: stability, planar sections in ℓ1,
    Ann. Probab. 50 (2022), no. 6, 2344-2372. [pdf]

  • G. Chasapis, K. Gurushankar, T. Tkocz,
    Sharp bounds on p-norms for sums of independent uniform random variables, 0 < p < 1,
    J. Anal. Math. 149 (2023), no. 2, 529–553. [pdf]

  • A. Havrilla, P. Nayar, T. Tkocz,
    Khinchin-type inequalities via Hadamard's factorisation,
    Int. Math. Res. Not. IMRN 2023, no. 3, 2429–2445. [pdf]

  • G. Chasapis, H. König, T. Tkocz,
    From Ball's cube slicing inequality to Khinchin-type inequalities for negative moments,
    J. Funct. Anal. 281 (2021), no. 9, Paper No. 109185, 23 pp. [pdf]

  • G. Chasapis, R. Liu, T. Tkocz,
    Rademacher- Gaussian tail comparison for complex coefficients and related problems,
    Proc. Amer. Math. Soc. 150 (2022), no. 3, 1339–1349. [pdf]

  • A. Frieze, T. Tkocz,
    Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects,
    Oper. Res. Lett. 49 (2021), no. 3, 400–404. [pdf]

  • A. Frieze, T. Tkocz,
    Shortest paths with a cost constraint: a probabilistic analysis,
    Discrete Appl. Math. 302 (2021), 46–53. [pdf]

  • D. Chakraborti, T. Tkocz, B.-H. Vritsiou
    A note on volume thresholds for random polytopes,
    Geom. Dedicata 213 (2021), 423–431. [pdf]

  • A. Frieze, W. Pegden, T. Tkocz,
    Random volumes in d-dimensional polytopes,
    Discrete Anal. 2020, Paper No. 15, 17 pp. [pdf]

  • P. Lamkin, T. Tkocz,
    Log-concavity and log-convexity of moments of averages of i.i.d. random variables,
    Canad. Math. Bull. 65 (2022), no. 2, 271–278. [pdf]

  • A. Havrilla, T. Tkocz,
    Sharp Khinchin-type inequalities for symmetric discrete uniform random variables,
    Israel J. Math. 246 (2021), no. 1, 281–297. [pdf]

  • A. Frieze, W. Pegden, G. Sorkin, T. Tkocz,
    Minimum-weight combinatorial structures under random cost-constraints,
    Electron. J. Combin. 28 (2021), no. 1, Paper No. 1.20, 18 pp. [pdf]

  • A. Frieze, T. Tkocz,
    A randomly weighted minimum arborescence with a random cost constraint,
    Math. Oper. Res. 47 (2022), no. 2, 1664–1680. [pdf]

  • A. Frieze, T. Tkocz,
    A randomly weighted minimum spanning tree with a random cost constraint,
    Electron. J. Combin. 28 (2021), no. 1, Paper No. 1.22, 25 pp. [pdf]

  • H. Huang, B. A. Slomka, T. Tkocz, B.-H. Vritsiou,
    Improved bounds for Hadwiger's covering problem via thin-shell estimates,
    J. Eur. Math. Soc. (JEMS) 24 (2022), no. 4, 1431–1448. [pdf]

  • A. Frieze, W. Pegden, T. Tkocz,
    On random multi-dimensional assignment problems,
    Discrete Appl. Math. 287 (2020), 1–9. [pdf]

  • M. Madiman, P. Nayar, T. Tkocz,
    Sharp moment-entropy inequalities for symmetric log-concave distributions,
    IEEE Trans. Inform. Theory 67 (2021), no. 1, 81–94. [pdf]

  • M. Madiman, P. Nayar, T. Tkocz,
    Two remarks on generalized entropy power inequalities,
    Geometric aspects of functional analysis. Vol. II, 169–185, Lecture Notes in Math., 2266, Springer, Cham, 2020. [pdf]

  • A. Frieze, W. Pegden, T. Tkocz,
    On the cover time of the emerging giant,
    SIAM J. Discrete Math. 36 (2022), no. 3, 1687–1710. [pdf]

  • A. Bonami, R. Latała, P. Nayar, T. Tkocz,
    Bounds on moments of weighted sums of finite Riesz products,
    J. Fourier Anal. Appl. 26 (2020), no. 6, Paper No. 84, 31 pp. [pdf]

  • J. Melbourne, T. Tkocz,
    Reversals of Rényi entropy inequalities under log-concavity
    IEEE Trans. Inform. Theory 67 (2021), no. 1, 45–51. [pdf]

  • R. Liu, T. Tkocz,
    A note on the extremal noncentral sections of the cross-polytope,
    Adv. in Appl. Math. 118 (2020), 102031, 17 pp. [pdf]

  • P. Nayar, T. Tkocz,
    On a convexity property of sections of the cross-polytope,
    Proc. Amer. Math. Soc. 148 (2020), no. 3, 1271-1278. [pdf]

  • A. Frieze, T. Tkocz,
    Random graphs with a fixed maximum degree,
    SIAM J. Discrete Math. 34 (2020), no. 1, 53-61. [pdf]

  • A. Frieze, T. Tkocz,
    A note on log-concave random graphs,
    Electron. J. Combin. 26 (2019), no. 3, Paper 3.36, 9 pp. [pdf]

  • P. Ivanisvili, T. Tkocz,
    Comparison of moments of Rademacher chaoses,
    Ark. Mat., 57 (2019), 121–128. [pdf]

  • W. Bednorz, T. Tkocz,
    Stochastic dominance and weak concentration for sums of independent symmetric random vectors,
    Int. Math. Res. Not. IMRN 2020, no. 23, 8997–9010. [pdf]

  • A. Eskenazis, P. Nayar, T. Tkocz,
    Sharp comparison of moments and the log-concave moment problem,
    Adv. Math. 334 (2018) 389–416. [pdf]

  • A. Eskenazis, P. Nayar, T. Tkocz,
    Gaussian mixtures: entropy and geometric inequalities,
    Ann. Probab. 46(5) 2018, 2908–2945. [pdf]

  • P. Nayar, T. Tkocz,
    A multidimensional analogue of the Rademacher-Gaussian tail comparison,
    Proc. Amer. Math. Soc. 146 (2018), no. 1, 413-419. [pdf]

  • M. Strzelecka, M. Strzelecki, T. Tkocz,
    On the convex infimum convolution inequality with optimal cost function,
    ALEA Lat. Am. J. Probab. Math. Stat. 14 (2017), no. 2, 903–915. [pdf]

  • K. Ball, P. Nayar, T. Tkocz,
    A reverse entropy power inequality for log-concave random vectors,
    Studia Math. 235 (2016), no. 1, 17-30. [pdf]

  • R. Latała, T. Tkocz,
    A note on suprema of canonical processes based on random variables with regular moments,
    Electron. J. Probab. 20 (2015), no. 36, 1-17. [pdf]

  • E. Damek, R. Latała, P. Nayar, T. Tkocz,
    Two-sided bounds for L_p-norms of combinations of products of independent random variables,
    Stochastic Process. Appl. 125 (2015), no. 4, 1688-1713. [pdf]

  • W. Johnson, A. Nasseri, G. Schechtman, T. Tkocz,
    Injective Tauberian operators on L1 and operators with dense range on l,
    Canad. Math. Bull. 58 (2015), no. 2, 276-280. [pdf]

  • P. Nayar, T. Tkocz,
    A note on certain convolution operators,
    Geometric aspects of functional analysis, 405-412, Lecture Notes in Math., 2116, Springer, Cham, 2014. [pdf]

  • O. Guédon, P. Nayar, T. Tkocz,
    Concentration inequalities and geometry of convex bodies,
    IM PAN Lecture Notes, Vol. 2, Warsaw 2014. [pdf]

  • P.Nayar, T. Tkocz,
    S-inequality for certain product measures,
    Math. Nachr. 287 (2014), No. 4, 398-404. [pdf]

  • M. Smaczynski, T. Tkocz, M. Kus, K. Zyczkowski,
    Extremal spacings between eigenphases of random unitary matrices and their tensor products,
    Phys. Rev. E 88, 052902 (2013) [pdf]

  • T. Tkocz,
    A note on the tensor product of two random unitary matrices,
    Electron. Commun. Probab. 18 (2013), no. 16, 1–7. [pdf]

  • P. Nayar, T. Tkocz,
    The unconditional case of the complex S-inequality,
    Israel J. Math. 197 (2013), no. 1, 99–106. [pdf]

  • 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. [pdf]

  • T. Tkocz, M. Smaczynski, M. Kus, O. Zeitouni, K. Zyczkowski,
    Tensor Products of Random Unitary Matrices,
    Random Matrices: Theory and Applications, Vol. 1, No. 4 (2012) 1250009 (26 pages). [pdf]

  • T. Tkocz,
    An Upper Bound for Spherical Caps,
    Amer. Math. Monthly 119 (2012), no. 7, 606-607. [pdf]

  • P. Nayar, T. Tkocz,
    On a Loomis-Whitney type inequality for permutationally invariant unconditional convex bodies,
    Geometric Aspects of Functional Analysis, 327-333, Lecture Notes in Math., Vol. 2050, Springer, Berlin Heidelberg, 2012. [pdf]

  • T. Tkocz,
    Gaussian measures of dilations of convex rotationally symmetric sets in C^n,
    Elect. Comm. in Probab. 16 (2011), 38–49. [pdf]