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Modified Log-Sobolev Inequality for a Compact Pure Jump Markov Process with Degenerate Jumps

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Abstract

We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. As a result, we obtain concentration properties for empirical approximations of the process. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced by Galves and Löcherbach (J Stat Phys 151:896–921, 2013).

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Correspondence to Ioannis Papageorgiou.

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This article was produced as part of the activities of FAPESP Research, Innovation and Dissemination Center for Neuromathematics (Grant 2013/ 07699-0 , S. Paulo Research Foundation); This article is supported by FAPESP Grant (2017/15587-8)

Communicated by Eric A. Carlen.

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Papageorgiou, I. Modified Log-Sobolev Inequality for a Compact Pure Jump Markov Process with Degenerate Jumps. J Stat Phys (2020). https://doi.org/10.1007/s10955-020-02506-2

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Keywords

  • Brain neuron networks
  • Pure jump Markov processes
  • Modified log-Sobolev inequality
  • Concentration
  • Empirical approximations

Mathematics Subject Classification

  • 60K35
  • 26D10
  • 60G99