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A characterization of transportation-information inequalities for Markov processes in terms of dimension-free concentration by Lacker, Daniel; Yeung, Lane Chun is a scholarly article available to read on EtoBox.

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Inequalities between transportation costs and Fisher information are known to characterize certain concentration properties of Markov processes around their invariant measures. This note provides a new characterization of the quadratic transportation-information inequality $W_2I$ in terms of a dimension-free concentration property for i.i.d. (conditionally on the initial positions) copies of the underlying Markov process. This parallels Gozlan's characterization of the quadratic transportation-entropy inequality $W_2H$. The proof is based on a new Laplace-type principle for the operator norms of Feynman-Kac semigroups, which is of independent interest. Lastly, we illustrate how both our theorem and (a form of) Gozlan's are instances of a general convex-analytic tensorization principle.

Author

Lacker, Daniel; Yeung, Lane Chun

Published

2020

Language

EN