Year: 2016
Type: preprint
Abstract: We determine the classical and the non-central Wallach sets $W_0$ and $W$ by classical probabilistic methods. We prove the Mayerhofer conjecture on $W$. We exploit the fact that $(x_0,β)\in W$ if and only if $x_0$ is the starting point and $2β$ is the drift of a squared Bessel matrix process $X_t$ on the cone $\bar{Sym^+(\mathbf{R},p)}$. Our methods are based on the study of SDEs for the symmetric polynomials of $X_t$ and for the eigenvalues of $X_t$, i.e. the squared Bessel particle systems.
Source: arXiv (Cornell University)
Authors: Graczyk, Piotr, Malecki, Jacek
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2291843950