Speaker
Giuseppe Tenaglia
(Imperial college London)
Description
Perturbations of high-dimensional systems are notoriously delicate: even when their magnitude vanishes with the dimension, their cumulative effect may remain significant due to the curse of dimensionality.
We study a class of uncoupled noisy systems perturbed by the introduction of a hole whose size decreases as the dimension grows. Although the perturbation becomes asymptotically small, its impact is amplified by dimensional growth.
Exploiting the product structure through tensorization, we prove that, if the uncoupled dynamics is noisy enough, the perturbed dynamics admits an equilibrium measure that stays uniformly close in W 1,2 to that of the unperturbed system
Author
Giuseppe Tenaglia
(Imperial college London)