Birkhoff's version of Hilbert's metric and its applications in analysis

By Bas Lemmens, Roger D. Nussbaum. 2013

52 citations recorded by the source corpus.

This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos and M. Troyanov, European Mathematical Society Publishing House, Z\"urich.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c197e5ceabca5e8a636ff8d7961e9506e7670b3c

How researchers see this paper

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In Applied Mathematics

1. Arnaud Doucet
2. James Thornton
3. Jeremy Heng
4. Valentin De Bortoli
5. Marco Cuturi
6. G. Peyr'e
7. Victor M. Panaretos
8. Yoav Zemel

In Geometry and Topology

1. Arnaud Doucet
2. Valentin De Bortoli

Citations in the corpus

• Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, background): “When the state-space is discrete and finite (Franklin and Lorenz, 1989; Peyré and Cuturi, 2019) or in the case where p data and p prior are compactly supported (Chen et al., 2016), IPF converges at a geometric rate w.r.t. the Hilbert-Birkhoff metric, see Lemmens and Nussbaum (2014) for a definition.”