Tomasz Tkocz

About

Tomasz Tkocz is an Associate Professor at Carnegie Mellon University in the Department of Mathematical Sciences. His contact information includes an office in Wean Hall, Pittsburgh, PA, and an email address ttkocz@math.cmu.edu. The webpage indicates his involvement in academic activities such as teaching and research within the field of mathematics. No additional details about his research focus, background, or key contributions are provided in the given text.

Research topics

• Statistics
• Mathematics
• Discrete mathematics
• Mathematical analysis
• Statistical physics
• Thermodynamics
• Pure mathematics
• Applied mathematics
• Physics
• Combinatorics

Selected publications

• Two Remarks on Generalized Entropy Power Inequalities

  Lecture notes in mathematics · 2020 · 13 citations

  Senior authorCorresponding
  DOI

• Reversal of Rényi Entropy Inequalities Under Log-Concavity

  IEEE Transactions on Information Theory · 2020 · 13 citations

  Senior authorCorresponding

  We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis, and establish a sharp Rényi version for certain parameters in both the continuous and discrete cases.

  DOI

• Extremal sections and projections of certain convex bodies: a survey

  2023-07-10 · 9 citations

  book-chapterSenior author

  We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly ℓp-balls, by and onto lower-dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since then has seen the development of a variety of probabilistic and analytic methods, showcased in this chapter.

  PublisherDOI

• Resilience of cube slicing in ℓp

  Duke Mathematical Journal · 2024-11-15 · 3 citations

  articleSenior author

  Ball’s celebrated cube slicing theorem asserts that among hyperplane sections of the cube in Rn, the central section orthogonal to (1,1,0,…,0) has the greatest volume. We show that the same continues to hold for slicing ℓp balls when p>1015, as well as that the same hyperplane minimizes the volume of projections of ℓq balls for 1<q<1+10−12. This extends Szarek’s optimal Khinchin inequality which corresponds to q=1. These results thus address the resilience of the Ball–Szarek hyperplane in the ra…

  PublisherDOI

• Sharp bounds on p-norms for sums of independent uniform random variables, 0 &lt; p &lt; 1

  Journal d Analyse Mathématique · 2023-01-05 · 3 citations

  articleSenior authorCorresponding
  PublisherDOI

Recent grants

• Analytic, Geometric, and Probabilistic Aspects of High-Dimensional Phenomena

  NSF · $205k · 2020–2024

Frequent coauthors

• Piotr Nayar

  University of Warsaw

  82 shared

• Alan Frieze

  30 shared

• Alexandros Eskenazis

  University of Cambridge

  19 shared

• Giorgos Chasapis

  University of Crete

  19 shared

• Amir Bahman Nasseri

  18 shared

• William B. Johnson

  18 shared

• Gideon Schechtman

  Weizmann Institute of Science

  18 shared

• Wesley Pegden

  11 shared

Education

• Ph.D.

  University of Warwick

Similar researchers at Carnegie Mellon University

• Michael Youngh-57
• David Kinderlehrerh-45