All Questions

I am trying to compute the first variation of the functional $$\mathcal F(\rho) = \int_{\Omega} R(x;\rho) d\rho(x)$$ where $R$ is some function of $x$ that also depends on $\rho$. Here $\rho$ is a ...

In Chapter 8 of the book Gradient Flows In Metric Spaces and in the Space of Probability Measures by Ambrosio et al., the tangent space to the space of distributions on $X$ (let's say $X=\mathbb{R}^d$)...

I am reading the introduction of Chapter 10 in the book Gradient Flows by Ambrosio and his coauthors. As we have seen in Section 1.4, in the classical theory of subdifferential calculus for proper, ...

I’m trying to understand if, when I move the marginals of a Wasserstein geodesic along a contractive flow, the geodesic between the new probability measures is “near” to the geodesic connecting the ...

Let $\mu_0$ be a log-concave distribution on $\mathbb R^d$ and let $f:\mathbb R^d \to \mathbb R$ be $C^2$. Let $x_0$ be sampled uniformly at random from a log-concave distribution $\mu_0$, meaning ...