Variable Exponent Wasserstein Spaces: Stability of Entropy Convexity and Modified Rényi Entropy

Ambroise Soglo, Cyrille Combété, Koffi Wilfrid Houédanou +1

We study the Wasserstein space $\mathcal{P}(M)$ equipped with a distance $\Wp$ constructed from the Lagrangian $L(x,v)=|v{|}^{p(x)}$ where $p(x)=2+\epsilon (x)$ with $\epsilon$…