A large deviation principle is established for the Poisson-Dirichlet distribution when the mutation rate [theta] converges to zero. The rate function is identified explicitly, and takes on finite values only on states that have finite number of alleles. This result is then applied to the study...

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and gamma subordinators with the two parameters, [alpha] and [theta], corresponding to the stable component and the gamma...

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele model, and then generalized, through the projective limit...

In this paper we prove the existence and uniqueness of solutions of the nonlinear martingale problems associated with the nonlinear master equations of multitype particle systems. Existence is shown to hold under some weak growth conditions and a finite range condition, while uniqueness is...

Large deviation principles are established for the Fleming-Viot process with neutral mutation and with selection, and the associated equilibrium measures as the sampling rate approaches zero and when the state space is equipped with the weak topology. The path-level large deviation results...

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting...