Week 09.11.2026 – 15.11.2026

I will review some recent results on the directed polymer model in dimension d=2, which can be seen as a discretised version of the stochastic heat equation. Recent results have shown that, in a suitable (and subtle) critical window of parameters, the model converges to a disordered limit, namely the Critical 2D Stochastic Heat Flow (SHF) introduced by Caravenna, Sun and Zygouras. This SHF is a non-Gaussian stochastic process of measures on R^2, and a lot of its properties have been studied over the last years. In this talk, I will first take some time to explain the (idea of the) construction of the SHF and then review some of the recent advances. In particular, I will comment on recentworks in collaboration with F. Caravenna, N. Turchi and N. Zygouras, which study how the mass assigned by the SHF to a ball behaves, either as time goes to infinity or as the radius of the ball goes to 0.

TBA

I will highlight some principles of information partition for the assessment of parametric statistical models, before attempting a foundation of inference for the assessment of semiparametric and other highly-parametrised models. I will highlight the possibility, in some contexts, of avoiding the usual semiparametric considerations, which typically require estimation of nuisance components through kernel smoothing or basis expansion, with the associated difficulties of tuning-parameter choice that blur the distinction between estimation and model assessment. A key aspect of the present work is the inducement of replication under the postulated model. This can be cast in terms of some non-standard inferential separations, in the vein of ancillarity/co-ancillarity and sufficiency/co-sufficiency separations, allowing the replacement of out-of-sample prediction error as a criterion for semiparametric model assessment by a type of within-sample prediction error. Framed in this light are new formulations in example settings.