Excursion Decompositions in Statistical Physics

This 55-minute lecture by Avelio Sepúlveda from the Hausdorff Center for Mathematics explores excursion decompositions across various statistical physics models. Discover how fields can be represented as sums $\sum_n \mu_n \delta_n$, where $\mu_n$ are positive measures with disjoint supports and $\delta_n$ are i.i.d. fair signs. Examine both discrete and continuous versions of random walks, Ising models, Gaussian free fields, and XOR-Ising models through this mathematical framework. The presentation is based on collaborative research with Tomás Alcalde, Juhan Aru, and Titus Lupu.