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High-Dimensional Phenomena in Convex Geometry, and Random Matrix Theory

  • Author / Creator
    Tikhomirov, Konstantin E
  • This thesis is based on six papers.

  • Subjects / Keywords
  • Graduation date
    Spring 2016
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3PN8XX4V
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Citation for previous publication
    • K. E. Tikhomirov. The smallest singular value of random rectangular matrices with no moment assumptions on entries. Israel Journal of Mathematics, 2016. DOI: 10.1007/s11856-016-1287-8
    • K. Tikhomirov and P. Youssef, When does a discrete-time random walk in $R^n$ absorb the origin into its convex hull? 2015, arXiv:1410.0458, to appear in the Annals of Probability.
    • K. E. Tikhomirov, On the distance of polytopes with few vertices to the Euclidean ball, Discrete Comput. Geom. 53 (2015), no.1, 173-181.
    • K. E. Tikhomirov, The Randomized Dvoretzky's theorem in \ell^{\infty} and the chi-distribution, Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics, 2116 (2014), 455-463.
    • K. E. Tikhomirov, Almost Euclidean sections in symmetric spaces and concentration of order statistics, J. Funct. Anal. 265 (2013), no.9, 2074-2088.
    • K. Tikhomirov, The limit of the smallest singular value of random matrices with i.i.d. entries, Adv. Math. 284 (2015), 1-20.
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)