Luca Dall'Asta — Politecnico di Torino #
Small-coupling dynamic cavity method for stochastic dynamics on sparse graphs #
In this seminar, I will present recent developments of the dynamic cavity method for stochastic dynamics on sparse graphs, with a particular focus on the weak-coupling regime. Starting from a graphical-model representation of interacting stochastic processes, the approach yields self-consistent equations for dynamical marginals and correlations on locally tree-like networks. A perturbative small-coupling expansion leads to a scalable Gaussian closure, closely related to dynamical mean-field theory.

I will then discuss two applications of the method. First, in the context of Bayesian epidemic inference, it provides efficient algorithms that consistently account for the non-causal effects induced by observations, allowing scalable estimation of individual infection risks and hidden epidemic trajectories on sparse contact networks.
Second, I will show how the same formalism can be applied to random generalized Lotka–Volterra equations, showing that sparse interactions qualitatively modify the stability and collective behavior of random ecosystems.