Essential spectral radius for Markov semigroups (I): discrete time case

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Transportation-information inequalities for Markov processes (2007, methodology): “Lyapunov conditions are widely used to study the speed of convergence of Markov chains [33] or Markov processes [18], large or moderate deviations and essential spectral radii [45, 47].”
A non‐conservative Harris ergodic theorem (2019, background): “a dissipativity condition which is closely related to (A1), see [94], and a compactness condition which is replaced here by (A4).”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, methodology): “Lyapunov conditions are widely used to study the speed of convergence of Markov chains [41] or Markov processes [24, 23], large or moderate deviations and essential spectral radii [54, 27, 55] or sharp large deviations [32].”
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, methodology): “The fact that a Lyapunov condition furnishes some Poincar´e inequality in the symmetric case is already known see Wu [34, 36 ], but the techniques used by Wu are different and rely mainly on spectral ideas.”