Abstract
The Sinkorn theorem is proved using Brouwer’s fixed point theorem and the corresponding algorithm is then described and used to solve the distribution problem from Chap. 1. A connection with the Schrödinger bridge equations is presented.
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Notes
- 1.
Uniqueness is up to a multiple, i.e., \(\mu D_1\) and \(\mu ^{-1}D_2\) also verify the theorem.
- 2.
For a version of this problem and its convergence in infinite dimensions see [47].
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Gutiérrez, C.E. (2023). Sinkhorn’s Theorem and Application to the Distribution Problem. In: Optimal Transport and Applications to Geometric Optics. SpringerBriefs on PDEs and Data Science. Springer, Singapore. https://doi.org/10.1007/978-981-99-4867-3_3
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