| Título: | Stein's Method and the Multivariate CLT for Traces of Powers on the Compact Classical Groups |
| Autores: |
Döbler, Christian; Ruhr University Bochum Stolz, Michael; Ruhr University Bochum |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
random matrices, compact Lie groups, Haar measure, traces of powers, Stein's method, normal approximation, exchangeable pairs, heat kernel, power sum symmetric polynomials 15B52; 60F05 ; 60B15; 58J65 |
| Descripción: | Let $M$ be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix size $n$, the vector of traces of consecutive powers of $M$ tends to a vector of independent (real or complex) Gaussian random variables. Recently, Jason Fulman has demonstrated that for a single power $j$ (which may grow with $n$), a speed of convergence result may be obtained via Stein's method of exchangeable pairs. In this note, we extend Fulman's result to the multivariate central limit theorem for the full vector of traces of powers. |
| Idioma: | No aplica |
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