When a tagged tracer particle diffuses in a bath of similar-sized particles, it locally perturbs the bath, leading to spatial correlations that can be generically long-ranged. Understanding these tracer-bath correlations offers a powerful tool for probing the tracer statistics in such strongly correlated systems — however, their analytical treatment remains challenging due to the complex many-body nature of the problem. Indeed, while these correlations have been recently characterized for the simple exclusion process in one spatial dimension [1], much less is known for higher dimensions (d > 1), and beyond simple lattice models.

In this talk, I will address the tracer-bath correlations for both discrete (hard-core) and continuum (soft-core) interacting particle systems in d > 1, using macroscopic fluctuation theory, the Dean-Kawasaki framework, and particle-based numerical simulations. I will show how the comb lattice — a geometry that interpolates between d=1 and d=2 — provides physical insights into the role of spatial correlations [2]. Finally, I will reveal a seemingly universal power-law decay at large distances, shared by a broad class of interacting particle systems, despite the distinct nature of their interactions [3].

REFS:
[1] A. Grabsch, A. Poncet, P. Rizkallah, P. Illien, O. Bénichou, Sci. Adv. 8, eabm5043 (2022)
[2] T. Berlioz, D. Venturelli, A. Grabsch, O. Bénichou, J. Stat. Mech. (2024) 113208
[3] D. Venturelli, P. Illien, A. Grabsch, O. Bénichou, arXiv:2411.09326 (2024)