# Small noise limit and convexity for generalized incompressible flows, Schr"odinger problems, and optimal transport

arXiv: https://arxiv.org/abs/1810.12036 · HTML: https://mlsanity.com/paper/1810.12036/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)

## Abstract (arXiv)

This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br"odinger problem recently introduced by M. Arnaudon & al. [3], the multiphase Brenier model, and the multiphase Br"odinger problem. All of them involve the minimization of a kinetic action and/or a relative entropy of some path measures with respect to the reversible Brownian motion. As the viscosity parameter nu→ 0 we establish Gamma-convergence relations between the corresponding problems, and prove the convergence of the associated pressures arising from the incompressibility constraints. We also present new results on the time-convexity of the entropy for some of the dynamical interpolations. Along the way we extend previous results by H. Lavenant [30] and J-D. Benamou & al. [10].