Large deviation principles for some random combinatorial structures in population genetics and Brownian motion

Large deviation principles are established for some random combinatorial structures including the Ewens sampling formula and the Pitman sampling formula. A path-level large deviation principle is established for the former on the cadlag space D$(o, 1], R)$ equipped with the uniform convergence topology, and the rate function is the same as for a Poisson process justifying the Poisson process approximation for the Ewens sampling formula at the …