LA Probability Forum

UCLA, Math Sciences Room 6627

The extremal properties of logarithmically correlated random fields have been a subject of considerable interest in recent years. A picture that has emerged from the analysis of salient examples such as Branching Random Walk and Discrete Gaussian Free Field in Z^2 is that, in these systems, the suitably centered maximum tends in law to a randomly-shifted Gumbel random variable while the associated extremal process tends in law to a decorated Poisson point process with a random intensity measure. In this talk, we will study the hierarchical Discrete Gaussian (DG) model that distinguishes itself from the above by taking only integer values. We will show the same picture holds for the hierarchical DG-model, with the results factor in the discrete nature of the field. The proof will be based on renormalization group techniques with a tight coupling between the hierarchical DG-model and Gaussian Branching Random Walk. The talk is based on joint work with Marek Biskup.