### Abstract

Original language | English |
---|---|

Pages (from-to) | 370-401 |

Number of pages | 32 |

Journal | Linear algebra and its applications |

Volume | 578 |

DOIs | |

Publication status | Published - 1 Oct 2019 |

### Fingerprint

### Keywords

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

### Cite this

*Linear algebra and its applications*,

*578*, 370-401. https://doi.org/10.1016/j.laa.2019.05.020

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

Research output: Contribution to journal › Article › Research › peer-review

*Linear algebra and its applications*, vol. 578, pp. 370-401. https://doi.org/10.1016/j.laa.2019.05.020

}

TY - JOUR

T1 - Polynomial convolutions in max-plus algebra

AU - Rosenmann, Amnon

AU - Lehner, Franz

AU - Peperko, Aljosa

N1 - 32 pages

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Max-plus algebra

KW - Maxplus polynomial convolution

KW - Maxplus characteristic polynomial

KW - Hadamard product

U2 - 10.1016/j.laa.2019.05.020

DO - 10.1016/j.laa.2019.05.020

M3 - Article

VL - 578

SP - 370

EP - 401

JO - Linear algebra and its applications

JF - Linear algebra and its applications

SN - 0024-3795

ER -