Transformations of polynomial ensembles
In Modern Trends in Constructive Function Theory (D.P. Hardin, D.S. Lubinsky, and B. Simanek, eds.) Contemporary Mathematics 661 (2016), pp. 253-268 A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\frac{1}{Z_n} \, \prod_{j<k} (x_k-x_j) \...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
22.01.2015
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1501.05506 |
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| Summary: | In Modern Trends in Constructive Function Theory (D.P. Hardin,
D.S. Lubinsky, and B. Simanek, eds.) Contemporary Mathematics 661 (2016), pp.
253-268 A polynomial ensemble is a probability density function for the position of
$n$ real particles of the form $\frac{1}{Z_n} \, \prod_{j<k} (x_k-x_j) \, \det
\left[ f_k (x_j) \right]_{j,k=1}^n$, for certain functions $f_1, \ldots, f_n$.
Such ensembles appear frequently as the joint eigenvalue density of random
matrices. We present a number of transformations that preserve the structure of
a polynomial ensemble. These transformations include the restriction of a
Hermitian matrix by removing one row and one column, a rank-one modification of
a Hermitian matrix, and the extension of a Hermitian matrix by adding an extra
row and column with complex Gaussians. |
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| DOI: | 10.48550/arxiv.1501.05506 |