Absence of open strings in a lattice-free simulation of cosmic string formation

Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk, Since in three or more dimensions such walks are transient, this approach necessarily generates a population of open strings. To investigate whether open strings are an artifact of the lattice we develop an alternative lattice-free simulation of string formation, Replacing the lattice with a graph generated by a minimal dynamical model of a first-order phase transition we obtain results consistent with the hypothesis that the energy density in string is due to a scale-invariant Brownian distribution of closed loops alone.