All Questions

I've been reading about probability on manifolds. What bothers me is that there's no clear way to generalize the Gaussian distribution to manifolds. If we instead assign a probability distribution to ...

Let $X:\Omega\to (M,g)$ be a random variable taking values in a Riemannian manifold $(M,g)$ with the Riemannian volume form denoted by $dvol_g(x).$ We know that there's no standard way to generalize ...

Let $\mu$ be a probability distribution on $\mathbb R^d$ with "sufficiently regular" density $p$. Let $f:\mathbb R^d \to \mathbb R$ be a "sufficiently regular" function. Finally, ...

For a point on the unit sphere, we know the plane perpendicular to the line through the origin and the point cuts the sphere with a big circle. When the point moves along a sphere curve, the ...