Week 22.03.2026 – 28.03.2026

In this talk, I will introduce a generalisation of the Ising model called the $\varphi^4$ model, which was originally introduced in quantum field theory as the simplest candidate for a non-Gaussian theory. Its importance in statistical physics was highlighted by Griffiths and Simon, who observed that the $\varphi^4$ potential arises as the scaling limit of the fluctuations of the critical Ising model on the complete graph. I will describe how this connection to the Ising model leads to two new geometric representations of the $\varphi^4$ model, called the random tangled current expansion and the random cluster model. I will then explain how these representations can be used to prove that the phase transition of the $\varphi^4$ model is continuous in dimensions three and higher, and to obtain large-deviation estimates for spin averages in the supercritical regime. Based on joint works with Trishen Gunaratnam, Romain Panis and Franco Severo.

We propose methods for compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $\mu_{1:n}$, known $\sigma_{1:n}$, observations $Y_i \sim \Norm(\mu_i, \sigma_i^2)$, and known costs $K_i$, the decision maker chooses a subset $S
\subset [n]$ to maximize utility $\frac{1}{n}\sum_{i\in S} (\mu_i - K_i)$. Inspired by Stein's unbiased risk estimate (SURE), we introduce an almost-unbiased estimator, ASSURE, for the expected utility of a proposed decision rule. ASSURE selects a welfare‑maximizing rule within a pre‑specified class by optimizing the estimated welfare, thereby borrowing strength across noisy estimates. We show that, within the pre-specified class, ASSURE's decisions are asymptotically no worse than the optimal (infeasible) rule. We apply ASSURE to the selection of Census tracts for economic opportunity, the identification of discriminating firms, and the analysis of $p$-value decision procedures in A/B testing.