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
Brownian excursion Groeneboom (1983) and Pitman (1983) give decompositions of Brownian motion formula_5 in terms of i.i.d Brownian excursions and the least concave majorant (or greatest convex minorant) of formula_5. For an introduction to Itô's general theory of Brownian excursions and the Itô Poisson process of excursions, see Revuz and Yor (1994), chapter XII. The Brownian excursion area arises in connection with the enumeration of connected graphs, many other problems in combinatorial theory; see e.g.,, and the limit distribution of the Betti numbers of certain varieties in cohomology theory. Takacs (1991a) shows that formula_19 has density where formula_21 are the zeros of