Avelio Sepúlveda: Excursion decompositions in statistical physics

Abstract:

In this talk, I will discuss excursion decompositions in various models of statistical physics. By an excursion decomposition, we mean a representation of a field as a sum \(\sum_n \mu_n \sigma_n\), where the \(\mu_n\) are positive measures with disjoint supports and the \(\sigma_n\) are i.i.d. fair signs. The models to be discussed are both the discrete and continuous versions of the random walk, Ising model, Gaussian free field and the XOR-Ising model. This talk is based on joint work with Tomás Alcalde, Juhan Aru, and Titus Lupu.