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Convergence of the eigenvalue density for Laguerre beta ensembles on short scales

   
@article{EJP2638,
	author = {Philippe Sosoe and Percy Wong},
	title = {Convergence of the eigenvalue density for Laguerre beta ensembles on short scales},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Ranbom Matrices, Beta Ensembles, Marchenko-Pastur law},
	abstract = {In this note, we prove that the normalized trace of the resolvent of the beta-Laguerre ensemble eigenvalues is close to the Stieltjes transform of the Marchenko-Pastur (MP) distribution with very high probability, for values of the imaginary part greater than $m^{1+\varepsilon}$. As an immediate corollary, we obtain convergence of the one-point density to the MP law on short scales. The proof serves to illustrate some simplifications of the method introduced in our previous work to prove a local semi-circle law for Gaussian beta-ensembles.},
	pages = {no. 34, 1-18},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-2638},    
        url = {http://ejp.ejpecp.org/article/view/2638}}