• Corpus ID: 218595973

Non-linear Log-Sobolev inequalities for the Potts semigroup and applications to reconstruction problems

@article{Gu2020NonlinearLI,
  title={Non-linear Log-Sobolev inequalities for the Potts semigroup and applications to reconstruction problems},
  author={Yuzhou Gu and Yury Polyanskiy},
  journal={ArXiv},
  year={2020},
  volume={abs/2005.05444}
}
Consider a Markov process with state space $[k]$, which jumps continuously to a new state chosen uniformly at random and regardless of the previous state. The collection of transition kernels (indexed by time $t\ge 0$) is the Potts semigroup. Diaconis and Saloff-Coste computed the maximum of the ratio of the relative entropy and the Dirichlet form obtaining the constant $\alpha_2$ in the $2$-log-Sobolev inequality ($2$-LSI). In this paper, we obtain the best possible non-linear inequality… 

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