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It is not, however, a good invariant even in the monogenic case: it is a consequence of results outlined at the Luminy conference that in the (monogenic) equal-characteristic case,
assumed to be continuous, the corresponding Markov chain will have the weak Feller property. The fact that a process is topologically recurrent also implies that.. it has some
Since its intrinsic metric of this Dirichlet form is just the L 2 -Wasserstein distance on P , this process is usually called Wasserstein diffusion... We shall only prove (i), and
set V of all total orders is compact and metrisable in its natural topology, and a probability measure µ on V is called exchangeable if it is invariant under the canonical action of
We do not pretend to remedy here to this extremely difficult problem, which ultimately should start from a Navier-Stokes type model and the analysis of its invariant measures.
sequences, and so Aldous’ question becomes one of whether or not we can identify the mixing probability measure associated with an exchangeable sequence given the distribution of
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan- tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P. Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can
