Teodor Banica, Ion Nechita
Published 2011-05-12, updated 2012-02-07Version 2
We study the partial transposition ${W}^\Gamma=(\mathrm{id}\otimes \mathrm{t})W\in M_{dn}(\mathbb C)$ of a Wishart matrix $W\in M_{dn}(\mathbb C)$ of parameters $(dn,dm)$. Our main result is that, with $d\to\infty$, the law of $m{W}^\Gamma$ is a free difference of free Poisson laws of parameters $m(n\pm 1)/2$. Motivated by questions in quantum information theory, we also derive necessary and sufficient conditions for these measures to be supported on the positive half line.
Journal: J. Theoret. Probab. 26 (2013), 855-869
Cutpoints of (1,2) and (2,1) random walks on the lattice of positive half line
Local time of transient random walk on the lattice of positive half line
On a maximum of nearest-neighbor random walk with asymptotically zero drift on lattice of positive half line
![QR code for arXiv:1105.2556 [math.PR]](http://oss.arxitics.com/images/favicon.svg)