Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population Lee, Ji Schnelli, Kevin ; https://orcid.org/0000-0003-0954-3231 We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where the sample X is an M ×N random matrix whose entries are real independent random variables with variance 1/N and whereσ is an M × M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class of populations σ in the sub-critical regime, we show that the distribution of the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians or (2) that σ is diagonal and that the entries of X have a sub-exponential decay. Institute of Mathematical Statistics 2016 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1157 Lee J, Schnelli K. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. <i>Annals of Applied Probability</i>. 2016;26(6):3786-3839. doi:<a href="https://doi.org/10.1214/16-AAP1193">10.1214/16-AAP1193</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1214/16-AAP1193 info:eu-repo/semantics/altIdentifier/wos/000391240100016 info:eu-repo/semantics/altIdentifier/arxiv/1409.4979 info:eu-repo/semantics/openAccess