The dynamics of fermionic many-body systems is investigated in the framework of Boltzmann–Langevin (BL) stochastic one-body approaches. Within the recently introduced Boltzmann–Langevin one-body (BLOB) model, we examine the interplay between mean-field effects and two-body correlations, of stochastic nature, for nuclear matter at moderate temperature and in several density conditions, corresponding to stable or mechanically unstable situations. Numerical results are compared with analytic expectations for the fluctuation amplitude of isoscalar and isovector densities, probing the link to the properties of the employed effective interaction; namely, symmetry energy (for isovector modes) and incompressibility (for isoscalar modes). For unstable systems, clusterization is observed. The associated features are compared with analytical results for the typical length and timescales characterizing the growth of unstable modes in nuclear matter and for the isotopic variance of the emerging fragments. We show that the BLOB model is generally better suited than simplified approaches previously introduced to solve the BL equation, and it is therefore more advantageous in applications to open systems, such as heavy-ion collisions.