Stochastic simulations on manifolds usually are traced back to Rn via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry. © 1994.
Schindler, W. (1994). Equivariant mappings: a new approach in stochastic simulations. Computational Geometry: Theory and Applications, 4(6), 327–343. https://doi.org/10.1016/0925-7721(94)00012-3