Mark Meckes's papers

Random matrix theory

• Random matrices with prescribed eigenvalues and expectation values for random quantum states (with E. Meckes).
  arXiv
• A sharp rate of convergence for the empirical spectral measure of a random unitary matrix (with E. Meckes).
  Zapiski Nauchnykh Seminarov POMI 457 (2017), 276–285 / Journal of Mathematical Sciences.
  arXiv / published version
• Rates of convergence for empirical spectral measures: a soft approach (with E. Meckes).
  Convexity and Concentration, 157–181, IMA Volumes in Mathematics and its Applications 161, Springer, 2017.
  arXiv / published version
• Self-similarity in the circular unitary ensemble (with E. Meckes).
  Discrete Analysis, 2016:9, 15 pp.
  arXiv / journal's editorial introduction (published version is on the arXiv)
• A rate of convergence for the circular law for the complex Ginibre ensemble (with E. Meckes).
  Ann. Fac. Sci. Toulouse Math. Series 6, 24 (2015) no. 1, 93–117.
  arXiv / published version
• Spectral measures of powers of random matrices (with E. Meckes).
  Electron. Commun. Probab. 18 (2013) no. 78, 1–13.
  arXiv / published version
• Concentration and convergence rates for spectral measures of random matrices (with E. Meckes).
  Probab. Theory Related Fields 156 (2013), 145–164.
  arXiv / published version
• The spectra of random abelian G-circulant matrices.
  ALEA Lat. Am. J. Probab. Math. Stat. 9 (2012) no. 2, 435–450.
  arXiv / published version
• Concentration for noncommutative polynomials in random matrices (with S. Szarek).
  Proc. Amer. Math. Soc. 140 (2012), 1803–1813.
  arXiv / published version
• Another observation about operator compressions (with E. Meckes).
  Proc. Amer. Math. Soc. 139 (2011), 1433–1439.
  arXiv / published version
• Some results on random circulant matrices.
  High Dimensional Probability V: The Luminy Volume, 213–223, IMS Collections 5, Institute of Mathematical Statistics, Beachwood, OH, 2009.
  arXiv / published version
• On the spectral norm of a random Toeplitz matrix.
  Electron. Commun. Probab. 12 (2007), 315–325.
  arXiv / published version
• Concentration of norms and eigenvalues of random matrices.
  J. Funct. Anal. 211 (2004) no. 2, 508–524.
  arXiv / published version

Magnitude and diversity

• The magnitude of a metric space: from category theory to geometric measure theory (with T. Leinster).
  Measure Theory in Non-Smooth Spaces, 156–193, DeGruyter Open, 2017.
  arXiv / published version
• Maximizing diversity in biology and beyond (with T. Leinster).
  Entropy 18 (2016) no. 3, article 88.
  arXiv / published version
  Note: Due to the journal's editorial policy, the numbering of theorems, examples, etc. in this paper was changed between the arXiv preprint and the published version.
• Magnitude, diversity, capacities, and dimensions of metric spaces.
  Potential Anal. 42 (2015) no. 2, 549–572.
  arXiv / published version
• Positive definite metric spaces.
  Positivity 17 (2013) no. 3, 733–757.
  arXiv / published version
  Note: The last paragraph of the published version of misstates the consequences for magnitude dimension of Theorems 4.4 and 4.5. The discussion around those results has been revised in the arXiv version to clarify this matter.

Probability in convexity and convexity in probability

• On the equivalence of modes of convergence for log-concave measures (with E. Meckes).
  Geometric Aspects of Functional Analysis, 385–394, Lecture Notes in Math. 2116, Springer, 2014.
  arXiv / published version
• Gaussian marginals of convex bodies with symmetries.
  Beiträge Algebra Geom. 50 (2009) no. 1, 101–118.
  arXiv / published version
• The central limit problem for random vectors with symmetries (with E. Meckes).
  J. Theoret. Probab. 20 (2007), 697–720.
  arXiv / published version
  Note: The arXiv preprint contains a section on background on Stein's method which does not appear in the published version. As a result, some theorem numbers are different in the two versions.
• Some remarks on transportation cost and related inequalities.
  Geometric Aspects of Functional Analysis, 237–244, Lecture Notes in Math. 1910, Springer, 2007.
  arXiv / published version
• Sylvester's problem for symmetric convex bodies and related problems.
  Monatsh. Math. 145 (2005) no. 4, 307–319.
  arXiv / published version
  Note: The published version contains several references to the literature which are missing in the arXiv preprint, and has improved proofs of Propositions 13 and 16.
• Volumes of symmetric random polytopes.
  Arch. Math. 82 (2004) no. 1, 85–96.
  arXiv / published version