Full absorption statistics of diffusing particles with exclusion

Suppose that an infinite lattice gas of constant density n₀, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius R. Employing the macroscopic fluctuation theory and assuming the additivity principle, we evaluate the probability distribution $P\left(N\right)$ that N particles are absorbed during a long time T. The limit of N = 0 corresponds to the survival problem, whereas $N\gg \overline{N}$ describes the opposite extreme. Here $\overline{N}=4\pi R{D}_0{n}_{0}T$ is the average number of absorbed particles (in three dimensions), and D₀ is the gas diffusivity. For n₀ ≪ 1 the exclusion effects are negligible, and $P\left(N\right)$ can be approximated, for not too large N, by the Poisson distribution with mean $\overline{N}$. For finite n₀, $P\left(N\right)$ is non-Poissonian. We show that $-\ln P\left(N\right)\simeq n_0{N}^2/\overline{N}$ at $N\gg \overline{N}$. At sufficiently large N and n₀ < 1/2 the most likely density profile of the gas, conditional on the absorption of N particles, is non-monotonic in space. We also establish a close connection between this problem and that of statistics of current in finite open systems. (paper)