We prove that a stochastic process of pure coagulation has at any timet ≥ 0 a time-dependent Gibbs distribution if and only if therates ψ(i, j) of single coagulations are of the formψ(i; j) = if(j) + jf(i), wheref is an arbitrary nonnegative function on the set of positive integers.We also obtain a recurrence relation for weights of these Gibbs distributionsthat allow us to derive the general form of the solution and the explicitsolutions in three particular cases of the function f. For the threecorresponding models, we study the probability of coagulation into one giantcluster by time t > 0.
"Coagulation processes with Gibbsian time evolution." J. Appl. Probab. 49 (3) 612 - 626, September 2012. https://doi.org/10.1239/jap/1346955321