# Transition Functions of Diffusion Processes on the Thoma Simplex

@article{Korotkikh2020TransitionFO, title={Transition Functions of Diffusion Processes on the Thoma Simplex}, author={Sergei Korotkikh}, journal={Functional Analysis and Its Applications}, year={2020}, volume={54}, pages={118-134} }

The paper deals with a three-dimensional family of diffusion processes on an infinite-dimensional simplex. These processes were constructed by Borodin and Olshanski in 2009 and 2010, and they include, as limit objects, the infinitely-many-neutral-allels diffusion model constructed by Ethier and Kurtz in 1981 and its extension found by Petrov in 2009. Each process X in our family possesses a unique symmetrizing measure M, called the z-measure. Our main result is that the transition function of X…

## 3 Citations

### The Topological Support of the z-Measures on the Thoma Simplex

- MathematicsFunctional Analysis and Its Applications
- 2018

The Thoma simplex Ω is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are probability measures on Ω depending on three continuous parameters. One…

### Transition Density of an Infinite-dimensional diffusion with the Jack Parameter

- Physics
- 2021

An infinite-dimensional diffusion with the Jack parameter is constructed by Olshanski in [16], and an explicit transition density is also obtained by Korotkikh through eigen expansion in [13]. We…

### The variance of the number of sums of two squares in [inline-graphic 01] [T] in short intervals

- MathematicsAmerican Journal of Mathematics
- 2021

Consider the number of integers in a short interval that can be represented as a sum of two squares. What is an estimate for the variance of these counts over random short intervals? We resolve a…

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