Probability and Mathematical Physics Seminar

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Multiscale Analysis of Wave Propagation in Random Media

Speaker: Josselin Garnier, École Polytechnique

Location: Warren Weaver Hall 1302

Date: Friday, October 30, 2026, 11 a.m.

Synopsis:

Wave propagation through complex media is strongly affected by small-scale random heterogeneities, which induce scattering, loss of coherence, and fluctuations of the wave field. Multiscale analysis provides effective stochastic models that describe these phenomena.
I will first consider propagation in a random medium in the paraxial regime, where a diffusion approximation leads to an Itô–Schrödinger equation and radiative transfer equations for the wave energy. I will then discuss randomly perturbed waveguides, where scattering couples guided modes and induces leakage into radiating modes. While the usual long-range regime leads to Gaussian field statistics, mode-dependent leakage in waveguides can produce exponentially growing relative intensity fluctuations and strongly non-Gaussian statistics. These results illustrate how geometry can fundamentally alter the statistical behavior of waves in random media.