Blockage of pores by particles is found in many processes, including filtration and oil extraction. We present filtration experiments through a linear array of ten channels with one dimension which is sub-micron, through which a dilute dispersion of Brownian polystyrene spheres flows under the action of a fixed pressure drop. The growth rate of a clog formed by particles at a pore entrance systematically increases with the number of already saturated (entirely clogged) pores, indicating that there is an interaction or "cross-talk" between the pores. This observation is interpreted based on a phenomenological model, stating that a diffusive redistribution of particles occurs along the membrane, from clogged to free pores. This one-dimensional model could be extended to two-dimensional membranes.