Near criticality, binary mixtures exhibit large composition fluctuations with spatial correlations. Introducing mobile catalysts that promote interconversion between the two components is expected to drive the system out of equilibrium, potentially altering its fluctuation spectrum. Understanding how such diffusing reactive agents, whose dynamics and coupling to the underlying fields can be represented explicitly, modify spatial correlations is the central objective of this project. The internship will focus on constructing and analyzing a theoretical model describing a near-critical binary mixture coupled to mobile catalysts. The mixture will be represented by continuous concentration fields obeying model B (conserved) stochastic dynamics derived from a Gaussian free energy. Catalysts will be modeled as diffusing sources and sinks that locally bias the A ↔ B conversion reaction. Analytical methods (such as stochastic field theories, Langevin equations, perturbative expansion) will be used to determine how catalyst motion modifies the two-point correlations of the fields. Particular attention will be paid to identifying possible long-range, non-equilibrium correlations emerging from the interplay between diffusion and reaction, and to investigating their consequence on tracer diffusion and fluctuation-induced forces, like the one evidenced recently in externally driven systems.