On Gaussian triangular arrays in the case of strong dependence (Q6635937)

Let \(\{\xi_{i,n},i=1,\ldots,n\}_{n\geq1}\) be a triangular array of random variables, where the random variables in each row have a multivariate Gaussian distribution. Letting \(M_n^*=\max_{1\leq i\leq n}\xi_{i,n}\), the author shows that, under suitable boundedness conditions, the distribution function of a normalised version of \(M_n^*\) converges to a Gaussian mixture of Gumbel distributions as \(n\to\infty\). A detailed discussion and comparison to existing results is included, compared to which the main advantage in the present paper is the removal of conditions of stationarity.