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Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array ofindependent $\mathbb{R}^d$-valued Gaussian random vectors with correlationmatrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wisemaxima converge to some max-stable distribution which generalizes the class ofH\"{u}sler-Reiss distributions. In the bivariate case, the conditions will alsobe sufficient. Using these results, new models for bivariate extremes arederived explicitly. Moreover, we define a new class of stationary, max-stableprocesses as max-mixtures of Brown-Resnick processes. As an application, weshow that these processes realize a large set of extremal correlationfunctions, a natural dependence measure for max-stable processes. This setincludes all functions $\psi(\sqrt{\gamma(h)}),h\in \mathbb{R}^d$, where $\psi$is a completely monotone function and $\gamma$ is an arbitrary variogram.

Maxima of independent, non-identically distributed Gaussian vectors