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The goal of this talk is to show that strong correlations between particles may emerge dynamically due to a common stochastically fluctuating environment, even when there is no direct built-in interaction between particles. These correlations grow with time, eventually driving the system into a `strongly correlated' nonequilibrium stationary state with nontrivial properties. I will demonstrate this in an exactly solvable model of noninteracting Brownian particles in a harmonic trap whose stiffness switches between two values at a constant rate. This model has been recently realized experimentally in optically trapped colloidal particle systems. Experimental results agree very well with theoretical predictions. Recording during the thematic meeting : «Random walks: applications and interactions» the January 19, 2026 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area