Markov Processes on the Thoma Simplex

Student: Korotkikh Sergei

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2018

The paper deals with a three-dimensional family of diffusion processes on an infinite-dimensional simplex. These processes were constructed by Borodin and Olshanski (2009; 2010), and they include, as limit objects, Ethier-Kurtz's infinitely-many-neutral-allels diffusion model (1981) and its extension found by Petrov (2009). Each process X from our family possesses a symmetrising measure M. Our main result is that the transition function of X has continuous density with respect to M. This is a generalization of earlier results due to Ethier (1992) and to Feng, Sun, Wang, and Xu (2011). Our proof substantially uses a special basis in the algebra of symmetric functions related to Laguerre polynomials.

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