Rate of convergence in probability to the Marchenko-Pastur law

By Friedrich Götze, A. Tikhomirov. 2004

107 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/00daab0ca6624d5fe2aae327ece3d2daa09ec908

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Van H. Vu
2. Terence Tao
3. Jun Yin
4. Natesh S. Pillai
5. L. Erdős
6. Debashis Paul
7. Alexander Aue
8. Friedrich Götze

In Statistics and Probability

1. Van H. Vu
2. Terence Tao
3. Jun Yin
4. Alexander Aue
5. Debashis Paul
6. Natesh S. Pillai
7. Friedrich Götze
8. L. Erdős

Citations in the corpus

• The rate of convergence for spectra of GUE and LUE matrix ensembles (2005, background): “[6] and Götze and Tikhomirov [18] showed that ∆ (m) n = O(n− 1 2 ).”
• The spectral norm of random inner-product kernel matrices (2015, background): “[50, 30, 55, 26, 45] as well as the recent work of [52, 19] in a nonindependent setting), the model (1) for nonlinear kernels does not have the same independence structure as these models, and it is also not a sum of rank-one updates.”
• Universality of covariance matrices (2011, background): “To our knowledge, there are two weaker versions of the above theorem previously established in [20, 14].”
• Random matrix theory in statistics: A review (2014, background): “In Götze and Tikhomirov (2003, 2004), for both Wigner and Wishart matrices, assuming sufficient number of moments for the entries, it was shown that as long as γ is away from 1, the rate of convergence of expected ESD and the ESD to the limiting ESD is Oðn 1=2Þ.”
• The Church of the Symmetric Subspace (2013, methodology): “When k = 2, ν(ψ) is simply the largest Schmidt value of a random state, and should be roughly (1/ √ d1 + 1/ √ d2) 2, according to the Marčenko-Pastur law [19].”
• Random covariance matrices: Universality of local statistics of eigenvalues (2009, background): “Further results are known on the rate of convergence: see [24].”
• Hippocampal Offline Reactivation Consolidates Recently Formed Cell Assembly Patterns during Sharp Wave-Ripples (2016, unknown): “%) with a significant negative slope.”