Fluctuations of absorption of interacting diffusing particles by multiple absorbers

We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via multiple receptors distributed over the cell surface. Employing the macroscopic fluctuation theory, we calculate the covariance matrix of the particle absorption by different patches, extending previous works which addressed fluctuations of a single current. We find a condition when the sign of correlations between different patches is fully determined by the transport coefficients of the gas and is independent of the problem's geometry. We show that the fluctuating particle flux field typically develops vorticity. We establish a simple connection between the statistics of particle absorption by all the patches combined and the statistics of current in a non-equilibrium steady state in one dimension. We also discuss connections between the absorption statistics and (i) statistics of electric currents in multi-terminal diffusive conductors and (ii) statistics of wave transmission through disordered media with multiple absorbers.