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- W2891528216 abstract "We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show that the canonical ensemble (ce) satisfies a uniform logarithmic Sobolev inequality (LSI). The LSI constant is uniform in the boundary data, the external field and scales optimally in the system size. This extends a classical result of H.T. Yau from discrete to unbounded, real-valued spins. It also extends prior results of Landim, Panizo & Yau or Menz for unbounded, real-valued spins from absent- or weak- to strong-interaction. The proof of the LSI uses a combination of the two-scale approach and a block-decomposition technique introduced by Zegarlinski. Main ingredients are the strict convexity of the coarse-grained Hamiltonian, the equivalence of ensembles and the decay of correlations in the ce. Those ingredients were recently provided by the authors." @default.
- W2891528216 created "2018-09-27" @default.
- W2891528216 creator A5020301249 @default.
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- W2891528216 date "2018-07-11" @default.
- W2891528216 modified "2023-09-27" @default.
- W2891528216 title "Uniform LSI for the canonical ensemble on the 1d-lattice with strong, finite-range interaction" @default.
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