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• W809944987 abstract "We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices $A = XX^*$, where $X$ is an $N times n$ matrix with iid standard complex normal entries. Under the scaling $n = N + lfloor sqrt{ 4 c N} rfloor$, $c > 0$ and $N rightarrow infty$, we show that the rescaled fluctuations of the smallest eigenvalue, largest eigenvalue and condition number of the matrices $A$ are all given by the Tracy--Widom distribution ($beta = 2$). This scaling is motivated by the study of the solution of the equation $Ax=b$ using the conjugate gradient algorithm, in the case that $A$ and $b$ are random: For such a scaling the fluctuations of the halting time for the algorithm are empirically seen to be universal." @default.
• W809944987 created "2016-06-24" @default.
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• W809944987 date "2015-07-02" @default.
• W809944987 modified "2023-09-27" @default.
• W809944987 title "On the condition number of the critically-scaled Laguerre Unitary Ensemble" @default.
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