Polynomial convolutions in max-plus algebra

Amnon Rosenmann, Franz Lehner, Aljosa Peperko

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielman and Srivastava and then Marcus studied certain combinatorial polynomial convolutions. These convolutions preserve real-rootedness and capture expectations of characteristic polynomials of unitarily invariant random matrices, thus providing a link to free probability. We explore analogues of these types of convolutions in the setting of max-plus algebra. In this setting the max-permanent replaces the determinant and the maximum is the analogue of the expected value. Our results resemble those of Marcus et al., however, in contrast to the classical setting we obtain an exact and simple description of all roots.
Original languageEnglish
Pages (from-to)370-401
Number of pages32
JournalLinear algebra and its applications
Volume578
DOIs
Publication statusPublished - 1 Oct 2019

Fingerprint

Max-plus Algebra
Convolution
Polynomial
Free Probability
Analogue
Interlacing
Characteristic polynomial
Random Matrices
Expected Value
Determinant
Roots
Invariant

Keywords

  • Max-plus algebra
  • Maxplus polynomial convolution
  • Maxplus characteristic polynomial
  • Hadamard product

Cite this

Polynomial convolutions in max-plus algebra. / Rosenmann, Amnon; Lehner, Franz; Peperko, Aljosa.

In: Linear algebra and its applications, Vol. 578, 01.10.2019, p. 370-401.

Research output: Contribution to journalArticleResearchpeer-review

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