Personal-Social Disequilibria in a Bureaucratic System

Maas, Henry S.; Prince, Charles H.; Davie, George

doi:10.1080/00332747.1953.11022918

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2017

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“…Another possibility is to consider finitely supported test functions. According to [25], this case may be covered by using the results of Daniri and Savaré [16]. We expect that the result below still holds for countable Markov chains, but we leave the proof for future works; also see [18,Remark 4.2].…”

Section: Examplesmentioning

confidence: 96%

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Discrete Beckner inequalities via the Bochner–Bakry–Emery approach for Markov chains

Jüngel¹,

Yue²

2017

Ann. Appl. Probab.

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Discrete convex Sobolev inequalities and Beckner inequalities are derived for time-continuous Markov chains on finite state spaces. Beckner inequalities interpolate between the modified logarithmic Sobolev inequality and the Poincaré inequality. Their proof is based on the Bakry-Emery approach and on discrete Bochner-type inequalities established by Caputo, Dai Pra, and Posta and recently extended by Fathi and Maas for logarithmic entropies. The abstract result for convex entropies is applied to several Markov chains, including birth-death processes, zero-range processes, Bernoulli-Laplace models, and random transposition models, and to a finite-volume discretization of a onedimensional Fokker-Planck equation, applying results by Mielke.

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Section: Examplesmentioning

confidence: 96%

“…Setting C 0 := (c x (η x ) − c x (η x − 1)) − (c y (η y + 1) − c y (η y )), the bounds (25) imply that |C 0 | ≤ δ. Hence, by Young's inequality,…”

Section: Examplesmentioning

confidence: 99%