2010/08/05 by Boris L. Granovsky, Granovsky, Boris, Alexander V. Kryvoshaev +1
Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1008.1027
openalex publication_date 2010/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that time dynamics of a stochastic process of pure coagulation is given by a time dependent Gibbs distribution if and only if rates of single coagulations have the form ψ(i,j)=if(j)+jf(i), where f is an arbitrary nonnegative function on the set of integers ≥ 1. We also obtained a recurrence relation for weights of these Gibbs distributions, that allowed explicit solutions in three particular cases of the function f. For the three corresponding models, we study the probability of coagulation into one giant cluster, at time t>0.