Concentration inequalities for polynomials of contracting Ising models

@article{Gheissari2017ConcentrationIF,
  title={Concentration inequalities for polynomials of contracting Ising models},
  author={Reza Gheissari and Eyal Lubetzky and Yuval Peres},
  journal={arXiv: Probability},
  year={2017}
}
We study the concentration of a degree-$d$ polynomial of the $N$ spins of a general Ising model, in the regime where single-site Glauber dynamics is contracting. For $d=1$, Gaussian concentration was shown by Marton (1996) and Samson (2000) as a special case of concentration for convex Lipschitz functions, and extended to a variety of related settings by e.g., Chazottes et al. (2007) and Kontorovich and Ramanan (2008). For $d=2$, exponential concentration was shown by Marton (2003) on lattices… Expand
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