Polynomial convolutions in max-plus algebra
| Autor: | Franz Lehner, Aljoša Peperko, Amnon Rosenmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Polynomial Algebra and Number Theory 010102 general mathematics 010103 numerical & computational mathematics Mathematics - Rings and Algebras Expected value Free probability 01 natural sciences Convolution Combinatorics Rings and Algebras (math.RA) FOS: Mathematics Discrete Mathematics and Combinatorics Hadamard product Canonical form Geometry and Topology 0101 mathematics Invariant (mathematics) Random matrix Mathematics |
| Popis: | 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, the maximum is the analogue of the expected value and real-rootedness is replaced by full canonical form. 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. 27 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|