Week 20.10.2025 – 26.10.2025

We study the response of an infinite system of point particles on the real line, initially at rest, to the instantaneous release of energy in a localized region. The blast generates shock fronts that travel sub-ballistically. The density, velocity, and temperature profiles in the growing region between the shock fronts can be obtained from exact self-similar solutions of the Euler equations. We compare these with the results of microscopic simulations. At long times, the results obtained from the simulations show a remarkable agreement with the predictions from Euler hydrodynamics except at the blast core where we show that corrections due to Navier-Stokes terms are important. We will also discuss the "splash" problem where energy is injected from one side of a semi-infinite cold gas.

Consider the first passage percolation distance on random planar maps, which is obtained by putting i.i.d. exponential random lengths on each (dual) edge. The study of this distance is often simpler than the study of the (dual) graph distance. I will describe a time-reversal of the uniform peeling exploration, which enables me to obtain the scaling limit of the number of faces along the geodesics to the root, to compare the metric balls for the first passage percolation and the dual graph distance and to upperbound the diameter of large random maps. Then, I will obtain the scaling limit of the tree of first passage percolation geodesics to the root via a stochastic coalescing flow of pure jump diffusions. This stochastic flow is also a tool to construct some random metric spaces which I conjecture to be the scaling limit of random planar maps with high degrees.

I will discuss a one-dimensional system of bosons or fermions with stochastic nearest-neighbor hopping, modeled as Brownian motion and driven out of equilibrium by boundary injection and removal processes. This setting defines the open Quantum Simple Symmetric Exclusion (QSSEP, for fermions) or Inclusion (QSSIP, for bosons) Process. For these noisy quantum systems, I will present results on the fluctuation statistics of density and current. For large system size, the corresponding large deviation functions are shown to converge with those of their classical counterparts, revealing a form of classical typicality emerging from quantum stochastic dynamics at large scales.

The characterization of the out-of-equilibrium dynamics of quantum many body systems is one of the most interesting challenges of modern quantum statistical physics: one of the main issues is to investigate quantities
and techniques which can encode huge amount of informations into a transparent form, giving insight into the physical properties of the system. For free systems evolving after a quantum quench, the quasiparticle picture has proven to be very effective at providing the evolution of several entropy-related quantities at the ballistic scale. In this talk I will discuss some recent work on a novel operatorial approach to the study of the quasiparticle picture, which allows to obtain effective hydrodynamic scale expressions for the dynamics of the entanglement hamiltonians and negativity hamiltonians, and also to easily extend the quasiparticle picture to novel configurations and quantities of interest, such as systems involving projective measurements. Finally, I will discuss tentative extensions to interacting integrable systems.

We introduce bandit importance sampling (BIS), a new class of importance sampling methods designed for settings where the target density is expensive to evaluate. In contrast to adaptive importance sampling, which optimises a proposal distribution, BIS directly designs the samples through a sequential strategy that combines space-filling designs with multi-armed bandits. Our method leverages Gaussian process surrogates to guide sample selection, enabling efficient exploration of the parameter space with minimal target evaluations. We establish theoretical guarantees on convergence and demonstrate the effectiveness of the method across a broad range of sampling tasks. BIS delivers accurate approximations with fewer target evaluations, outperforming competing approaches across multimodal, heavy-tailed distributions, and real-world applications to Bayesian inference of computationally expensive models.