In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements satisfying the so-called Lyapunov condition. Under an appropriated normalization, the joint law of the extremal singular values converges in distribution, as the matrix dimension tends to infinity, to an independent product of Rayleigh and Gumbel laws. The latter implies that a normalized condition number converges in distribution to a Fr\'echet law as the dimension of the matrix increases.

翻译：在这份手稿中,我们研究对随机循环剂基体的最大和最小单值联合法的有限分配,其生成顺序由独立和同样分布的随机要素给出,满足所谓的Lyapunov条件。在被分配的正常化下,极单值联合法在分配中趋于一致,因为矩阵层面往往无限,与Rayleigh和Gumbel法律的独立产品相融合。后者意味着随着矩阵层面的增加,正常条件数在分配上会与Fr\'echet法相融合。