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On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries

  
@article{EJP899,
	author = {Radoslaw Adamczak},
	title = {On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {random matrix, Marchenko-Pastur law, circular law, log-concave measures},
	abstract = {In the first part of the article we prove limit theorems of Marchenko-Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large numbers, uniform bounds on moments and a martingale like condition investigated previously by Goetze and Tikhomirov. Examples include log-concave unconditional distributions on the space of matrices.  In the second part  we specialize to random matrices with independent isotropic unconditional log-concave rows for which (using the Tao-Vu replacement principle) we prove the circular law.},
	pages = {no. 37, 1065-1095},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-899},    
        url = {http://ejp.ejpecp.org/article/view/899}}