The Volume of the Trace-Nonnegative Polytope via the Irwin-Hall Distribution
Metric Geometry
2016-03-23 v2 Combinatorics
Probability
Abstract
In this work, we find an explicit expression for the volume of the trace nonnegative polytope via a generalization of the Irwin-Hall distribution. This volume is an upper bound for the volume of all projected, normalized realizable spectra. We provide ancillary results on realizable trace-zero spectra and pose several problems suitable for further inquiry.
Keywords
Cite
@article{arxiv.1511.03700,
title = {The Volume of the Trace-Nonnegative Polytope via the Irwin-Hall Distribution},
author = {Pietro Paparella and Gregory K. Taylor},
journal= {arXiv preprint arXiv:1511.03700},
year = {2016}
}