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Regular version of the site
Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Sergei Korotkikh
Markov Processes on the Thoma Simplex
Mathematics
(Bachelor’s programme)
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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