Rosenmann, Amnon ; Lehner, Franz, matematik ; Peperko, Aljoša
Pred kratkim so v delu, ki je izšlo iz študija prepletajočih polinomov, Marcus, Spielman and Srivastava [Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava, Finite free convolutions of ...polynomials, arXiv :1504 .00350, 2015] in Marcus [Adam W. Marcus, Polynomial convolutions and (finite) free probability, preprint on webpage at https://web.math.princeton.edu/~amarcus/index.html, 2016] študirali določene kombinatorične polinomske konvolucije. Te konvolucije ohranjajo lastnost, da ima polinom realne ničle in opisujejo povprečja karakterističnih polinomov unitarno invariantnih naključnih matrik, kar povezuje tematiko s prosto verjetnostjo. V našem članku študiramo analoge teh konvolucij v okviru max-plus algebre. V tem okviru max-permanenta nadomešča determinanto,maksimum je analog povprečni vrednosti (integralu) in polna kanonična forma nadomešča lastnost posedovanja realnih ničel. Naši rezulatati so podobni rezultatom Marcusa in sodelovcev, vendar dobimo v kontrastu s klasično postavitvijo eksakten in enostaven opis vseh tropskih ničel konvolucije maxpolinomov ▫$p(x)$▫ in ▫$q(x)$▫ opisane s pomočjo tropskih ničel maxpolinomov ▫$p(x)$▫ in ▫$q(x)$▫.
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