We study the nucleation and growth of flame fronts in slow combustion.
This is modeled by a set of reaction-diffusion equations for the temp
erature held, coupled to a background of reactants and augmented by a
term describing random temperature fluctuations for ignition. We estab
lish connections between this model and the classical theories of nucl
eation and growth of droplets from a metastable phase. Our results are
in good agreement with theoretical predictions.