Concentration inequalities for dependent random variables via the martingale method

Leonid Kontorovich, Kavita Ramanan

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomoge-neous Markov chains and hidden Markov chains, and an extremal property associated with their martingale difference bounds is established. This work complements and generalizes certain concentration inequalities obtained by Marton and Samson, while also providing different proofs of some known results.

Original languageEnglish
Pages (from-to)2126-2158
Number of pages33
JournalAnnals of Probability
Issue number6
StatePublished - 1 Nov 2008
Externally publishedYes


  • Bounded martingale differences
  • Concentration inequality
  • Contracting markov chains
  • Hidden markov chains
  • Markov chains
  • McDiarmid's bound
  • Mixing coefficients


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