String Theory Journal Club

We define a stochastic process using simple, parameter-dependent entity aggregation rules with the possibility of disintegration of formed clusters, and derive the appropriate equations governing this process. We show that, with appropriate choice of dynamic parameters, the stationary distribution of cluster sizes is given by a solvable recurrence, which, after rescaling, takes the form of a Catalan-like recurrence. In particular, we demonstrate for which parameter values the given process reproduces various integer sequences, including the Catalan, Motzkin, and Schröder numbers.