Rotational Brownian motion (astronomy) supermassive black holes at the centers of galaxies. Perturbations from passing stars can alter the orbital plane of such a binary, which in turn alters the direction of the spin axis of the single black hole that forms when the two coalesce. Rotational Brownian motion is often observed in N-body simulations of galaxies containing binary black holes. The massive binary sinks to the center of the galaxy via dynamical friction where it interacts with passing stars. The same gravitational perturbations that induce a random walk in the orientation of the binary, also cause the binary to shrink, via the gravitational
Brownian surface Brownian motion, Brownian surfaces are named after 19th-century biologist Robert Brown. Efficient generation of fractional Brownian surfaces poses significant challenges. Since the Brownian surface represents a Gaussian process with a nonstationary covariance function, one can use the Cholesky decomposition method. A more efficient method is Stein's method, which generates an auxiliary stationary Gaussian process using the circulant embedding approach and then adjusts this auxiliary process to obtain the desired nonstationary Gaussian process. The figure below shows three typical realizations of fractional Brownian surfaces for different values of the roughness or Hurst parameter. The Hurst parameter is always between zero and