2018/07/11 by Younghak Kwon, Kwon, Younghak, Georg Menz +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.PR
paper · pdf · doi:10.48550/arxiv.1807.04333
35 pages
openalex publication_date 2018/07/11 · arxiv created 2019/11/30 · arxiv updated 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.