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Title: Extremes of stationary random fields on a lattice Authors:  Chengxiu Ling - Xi\'an Jiaotong-Liverpool University (China) [presenting]
Abstract: Extremal behavior of stationary Gaussian sequences/random fields is widely investigated since it models common cluster phenomena and brings a bridge between discrete and continuous extremes. We establish extensively limit theorems of stationary random fields under certain mixing and dependence conditions, which are further illustrated by typical examples of order statistics of Gaussian random fields and skew-Gaussian random fields. The positivity of the cluster index involved and its link with the expected cluster size are discussed.