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 ℓ_p,
  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 ℓ_p-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]