Abstract: We study the large scale limit of 2D Monte-Carlo simulations of
grain growth with isotropic grain boundary energy and mobility in the low
temperature regime and show that the Monte-Carlo model converges to the
deterministic Boundary Tracking model defined by the Mullins equation of
curvature driven growth and the Herring balance condition. The convergence
is illustrated by computer simulations at both the level of individual
grains and the level of distribution functions. The von Neumann's $(n-6)$
rule is verified for individual Monte-Carlo grains in an average sense and
a Fokker-Planck equation is shown to be useful in analyzing the distribution
functions in both the Monte-Carlo and the Boundary Tracking simulations.