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 all "t" ≥ 0, (with Φ the cumulative distribution function of the normal distribution) which yields (for "μ" < 0) when taking t → ∞ an exponential distribution For fixed "t", the distribution of "Z(t)" coincides with the distribution of the running maximum "M(t)" of the Brownian motion, But be aware that the distributions of the processes as a whole are very different. In particular, "M(t)" is increasing in "t", which is not the case for "Z(t)". The heat kernel for reflected Brownian motion at formula_9: formula_10 For the plane above formula_11 The stationary distribution of a reflected Brownian motion