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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 ...

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 ...

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 $\mu$ 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, ...