# Multi-marginal Entropy-Transport with repulsive cost

## TL;DR

This paper investigates the theoretical aspects of entropy-transport problems with repulsive costs, establishing existence, convergence, and duality results that deepen understanding of regularized multi-marginal optimal transport.

## Contribution

It provides new conditions for minimizer existence, proves $ ext{Gamma}$-convergence, and establishes duality for entropy-regularized multi-marginal transport with repulsive costs.

## Key findings

- Existence of minimizers under certain conditions
- Gamma-convergence of entropy-transport to multi-marginal optimal transport
- Entropy-regularized Kantorovich duality established

## Abstract

In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.