Rotational Brownian motion (astronomy) of supermassive black holes appear to be randomly aligned with respect to their host galaxies. Rotational Brownian motion (astronomy) In astronomy, rotational Brownian motion is the random walk in orientation of a binary star's orbital plane, induced by gravitational perturbations from passing stars. Consider a binary that consists of two massive objects (stars, black holes etc.) and that is embedded in a stellar system containing a large number of stars. Let formula_1 and formula_2 be the masses of the two components of the binary whose total mass is formula_3. A field star that approaches the binary with impact parameter formula_4
Reflected Brownian motion "roughly speaking, "Z" is pushed in direction "R" whenever the boundary surface formula_5 is hit, where "R" is the "j"th column of the matrix "R"." Stability conditions are known for RBMs in 1, 2, and 3 dimensions. "The problem of recurrence classification for SRBMs in four and higher dimensions remains open." In the special case where "R" is an M-matrix then necessary and sufficient conditions for stability are The marginal distribution (transient distribution) of a one-dimensional Brownian motion starting at 0 restricted to positive values (a single reflecting barrier at 0) with drift "μ " and variance "σ" is for