Abstract.
We consider reversible, conservative Ginzburg–Landau processes in a random environment, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. We prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L−2 almost surely with respect to the environment.
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Acknowledgement The authors wish to thank J. Quastel and H. T. Yau for the private communication of the unpublished manuscript [21]
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Landim, C., Noronha Neto, J. Poincaré and logarithmic Sobolev inequality for Ginzburg-landau processes in random environment. Probab. Theory Relat. Fields 131, 229–260 (2005). https://doi.org/10.1007/s00440-004-0370-y
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DOI: https://doi.org/10.1007/s00440-004-0370-y
Key words or phrases:
- Spectral Gap
- Logarithmic Sobolev Inequality
- Random Environment
Ann. Probab. 31, 115–147 (2003)