We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan’s melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy–Stefan problem.
@article{1147179989,
author = {Landim, Claudio and Valle, Glauco},
title = {A microscopic model for Stefan's melting and freezing problem},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 779-803},
language = {en},
url = {http://dml.mathdoc.fr/item/1147179989}
}
Landim, Claudio; Valle, Glauco. A microscopic model for Stefan’s melting and freezing problem. Ann. Probab., Tome 34 (2006) no. 1, pp. 779-803. http://gdmltest.u-ga.fr/item/1147179989/