The Annals of Probability

A microscopic model for Stefan’s melting and freezing problem

Claudio Landim and Glauco Valle

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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.

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Ann. Probab., Volume 34, Number 2 (2006), 779-803.

First available in Project Euclid: 9 May 2006

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Exclusion processes Cauchy–Stefan problem hydrodynamic limit


Landim, Claudio; Valle, Glauco. A microscopic model for Stefan’s melting and freezing problem. Ann. Probab. 34 (2006), no. 2, 779--803. doi:10.1214/009117905000000701.

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