Distances on circles, toruses and spheres
Bernard W. Silverman · Journal of Applied Probability · 1978
Families of heavily dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj) for some suitable function g of two arguments and independent uniformly distributed random variables Y1, Y2, ··· on the circle, the torus or the sphere. The weak convergence of the empirical distribution process is discussed. The particular case of distances between pairs of observations on the circle is considered in greater detail.