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The Poisson transport map

Year: 2025
Type: article
Abstract: We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities using transport maps in discrete settings, and allows us to deduce a number of functional inequalities for ultra-log-concave measures. In particular, we provide the currently best known constant in modified logarithmic Sobolev inequalities for ultra-log-concave measures.
DOI: 10.1016/j.jfa.2025.110864
Language: English
Open Access status: hybrid
Estimated APC paid: $3,250
Funders: National Science Foundation, Agence Nationale de la Recherche, Association Nationale de la Recherche et de la Technologie, Institut Universitaire de France, Horizon 2020, H2020 Marie Skłodowska-Curie Actions, HORIZON EUROPE Marie Sklodowska-Curie Actions
Awards: Measure Transportation And Notions Of Dimensionality In High Dimensional Probability, G5418794627, G574042872, PostDoctoral Research Fellowship, Convergence and Interactions via Analysis and Probability, Université de Paris
OpenAlex ID: W4407318699
FWCI: 1.87
Cites: 19
Cited by: 1
Related to: 10