Analysis of the extreme values for certain non-Gaussian and Gaussian fields, in particular the Ginzburg-Landau gradient interface model in d=2 and log-correlated Gaussian fields on percolation clusters using methods from renormalisation group theory.

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In my doctoral studies, I established convergence results for the global maximum of two distinguished Euclidean field theories, the sine-Gordon field and the Phi-4 field in d=2. To this end, I developed a set of tools to couple the field of interest with the well-studied Gaussian free field. In particular, this technique allows to compare the extreme values of both fields. There are many more examples to which my techniques apply, and it is my goal to establish a unified theory for their extreme values. Moreover, I will focus on related statistical fields, such as the Ginzburg-Landau gradient interface model and the Gaussian free field on disordered graphs, for which initial results already exists thanks to the work of my postdoctoral supervisor Ofer Zeitouni. Here, my goal is to adjust the renormalisation arguments to these different settings and answer some of the many open questions in this area. A crucial result that I hope to further exploit is the equivalence between the Polchinski renormalisation group approach and the Boue-Dupuis stochastic control representation, which I established in a recent project with N. Barashkov and T. Gunaratnam on the Phi-4 field.