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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 18:59:20 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 18:59:20 +0100 |
commit | 6b572dca1c4e53537352d9d4b09fccb637f392c9 (patch) | |
tree | a892504598298bc3a95b674e4a67f6d6dd78074e | |
parent | 96efa4aab61d26f673c725183d3da04a722da9ce (diff) | |
download | PRR_3_023064-6b572dca1c4e53537352d9d4b09fccb637f392c9.tar.gz PRR_3_023064-6b572dca1c4e53537352d9d4b09fccb637f392c9.tar.bz2 PRR_3_023064-6b572dca1c4e53537352d9d4b09fccb637f392c9.zip |
Make reference to complex Wishart.
-rw-r--r-- | bezout.tex | 10 |
1 files changed, 6 insertions, 4 deletions
@@ -152,10 +152,12 @@ is shifted by $p\epsilon$. The eigenvalue spectrum of the Hessian of the real part, or equivalently the eigenvalue spectrum of $(\partial\partial H)^\dagger\partial\partial H$, is the -singular value spectrum of $\partial\partial H$. This is a more difficult -problem and to our knowledge a closed form for arbitrary $\kappa$ is not known. -We have worked out an implicit form for this spectrum using the saddle point of -a replica calculation for the Green function. blah blah blah\dots +singular value spectrum of $\partial\partial H$. When $\kappa=0$ and the +elements of $J$ are standard complex normal, this corresponds to a complex +Wishart distribution. For $\kappa\neq0$ the problem changes, and to our +knowledge a closed form is not known. We have worked out an implicit form for +this spectrum using the saddle point of a replica calculation for the Green +function. blah blah blah\dots The transition from a one-cut to two-cut singular value spectrum naturally corresponds to the origin leaving the support of the eigenvalue spectrum. |