In the paper we solve the limit problem for partial maxima of m-dependent stationary random fields and we extend the obtained solution to fields satisfying some local mixing conditions. New methods for describing the limitting distribution of maxima are proposed. A notion of a phantom distribution function for a random field is investigated. As an application, several original formulas for calculation of the extremal index are provided. Moving maxima and moving averages as well as Gaussian fields satisfying the Berman condition are considered.

中文翻译：

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在渐近理论中管理局部依存关系，以获取平稳随机场的最大值

在本文中，我们解决了m依赖平稳随机场的局部最大值的极限问题，并将获得的解扩展到满足某些局部混合条件的场。提出了描述最大值极限分布的新方法。研究了用于随机场的幻影分布函数的概念。作为应用，提供了一些用于计算极值指数的原始公式。考虑满足伯曼条件的移动最大值和移动平均值以及高斯场。