“Scaling theory for gelation: A long standing riddle”

Irreversible aggregation sometimes leads to situations
in which an infinite aggregate is formed in a finite time and in a way
similar to what happens in percolation. In the mean-field approximation, the relevant description
parameters of the aggregation process are the reaction rates between aggregates as functions of their
respective masses. The main object of interest is the cluster size
distribution, which gives the concentration of
clusters of mass m at time t. The aim of scaling theory is to
provide a simplified description of the cluster size distribution
when t is very close to the critical time t__{c} at which the
infinite cluster appears, and when m is very large. Such theories have
been proposed since the eighties, but have clashed with numerical
evidence. I shall discuss the reasons for this discrepancy, as well as
recent attempts to resolve the issue.