  Diffusion-coagulation can be simply described by a dynamic where particles
perform a random walk on a lattice and coalesce with probability unity when
meeting on the same site. Such processes display non-equilibrium properties
with strong fluctuations in low dimensions. In this work we study this problem
on the fully-connected lattice, an infinite-dimensional system in the
thermodynamic limit, for which mean-field behaviour is expected. Exact
expressions for the particle density distribution at a given time and survival
time distribution for a given number of particles are obtained. In particular
we show that the time needed to reach a finite number of surviving particles
(vanishing density in the scaling limit) displays strong fluctuations and
extreme value statistics, characterized by a universal class of non-Gaussian
distributions with singular behaviour.
