Electronic Journal of Probability
- Electron. J. Probab.
- Volume 10 (2005), paper no. 29, 962-987.
Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation
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.
Electron. J. Probab., Volume 10 (2005), paper no. 29, 962-987.
Accepted: 18 July 2005
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
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