Electronic Journal of Probability

Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation

Gustavo Posta

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An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discrete gradient of the interface. The interaction Hamiltonian of the interface is given by a finite range part, proportional to the sum of height differences, plus a part of exponentially decaying long range potentials. The evolution of the interface is a reversible Markov process. We prove that if this system is started in the center of a box of size $L$ after a time of order $L^3$ it reaches, with a very large probability, the top or the bottom of the box.

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Electron. J. Probab., Volume 10 (2005), paper no. 29, 962-987.

Accepted: 18 July 2005
First available in Project Euclid: 1 June 2016

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Posta, Gustavo. Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation. Electron. J. Probab. 10 (2005), paper no. 29, 962--987. doi:10.1214/EJP.v10-270. https://projecteuclid.org/euclid.ejp/1464816830

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