Subordination processes for non-Gaussian diffusion: modelling and first passage phenomena

The motion of diffusive tracers in complex and disordered environments often deviates from classical Gaussian statistics associated with standard Brownian motion, instead exhibiting robust non-Gaussian behaviour, even when the mean squared displacement remains diffusive. Experimental, analytical and computational studies have linked such deviations to sample-to-sample variability and/or spatio-temporal heterogeneity intrinsic to these systems. I will present a general theoretical framework based on the concept of subordination that captures the emergence of non-Gaussian diffusion across a broad class of complex systems. Within this framework, two dynamical regimes, characterised by distinct scaling properties of the subordinator’s probability density function, naturally arise. Building on this formalism, I will show that, in the context of first-passage phenomena, Gaussian search strategies remain more effective in terms of the mean first-passage time. However, non-Gaussian dynamics can become markedly more efficient when only a small fraction of tracers is required to reach the target, leading to substantial deviations from Gaussian predictions. Finally, I will outline ongoing work and discuss future perspectives.