@article{AB-Intrinsic-Volumes-Of-Symmetric-Cones-And-Applications-In-Convex-Programming,
Title = {Intrinsic volumes of symmetric cones and applications in convex programming},
Author = {Dennis Amelunxen and Peter Bürgisser},
Pages = {105-130},
Year = {2015},
Journal = {Mathematical Programming},
Volume = {149},
Number = {1-2},
Note = {This is a substantially revised and shortened version of the paper "Intrinsic volumes of symmetric cones" [arXiv 1205.1863]},
Abstract = {We express the probability distribution of the solution of a random (standard Gaussian) instance of a convex cone program in terms of the intrinsic volumes and curvature measures of the reference cone. We then compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions in terms of integrals related to Mehta's integral. In particular, we obtain a closed formula for the probability that the solution of a random (standard Gaussian) semidefinite program has a certain rank.},
Url = {http://www3.math.tu-berlin.de/algebra/work/rev1-intrinsic-vols4.pdf},
Url2 = {http://link.springer.com/article/10.1007%2Fs10107-013-0740-2}
}