Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

Franck Barthe, Emanuel Milman
<span title="2013-08-14">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="" style="color: black;">Communications in Mathematical Physics</a> </i> &nbsp;
We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a
more &raquo; ... gly convex potential, this partially recovers and partially extends previous results of Caputo, Chafaï, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/s00220-013-1782-2</a> <a target="_blank" rel="external noopener" href="">fatcat:3xohukvwmvai7p4ef7645lfcu4</a> </span>
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