The Volume of the Trace-Nonnegative Polytope via the Irwin-Hall Distribution

2015/11/06 by Pietro Paparella, Paparella, Pietro, Gregory K. Taylor +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR) #math.CO #math.MG #math.PR

paper · pdf · doi:10.48550/arxiv.1511.03700

arxiv created 2016/03/22 · arxiv updated 2016/03/23

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.

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