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

Franck Barthe, Emanuel Milman

2013
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Communications in Mathematical Physics
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When the self-interaction is *a* perturbation *of* *a* strongly convex potential, this partially recovers and partially extends previous results *of* Caputo, Chafaï, Grunewald, Landim, Lu, Menz, Otto, Panizo, ...
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. ...
The asserted tail decay estimate now follows by *a* standard application *of* Chebyshev's inequality and optimization on p. ...

doi:10.1007/s00220-013-1782-2
fatcat:3xohukvwmvai7p4ef7645lfcu4