Geodesic
Tropical moments of tropical Jacobians
Canadian journal of mathematics, Tome 75 (2023) no. 4, pp. 1045-1075

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DOI

Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus is its tropical moment. We give an explicit and efficiently computable formula for the tropical moment of a tropical Jacobian in terms of potential theory on the underlying metric graph. We show that there exists a universal linear relation between the tropical moment, a certain capacity called the tau invariant, and the total length of a metric graph. To put our formula in a broader context, we relate our work to the computation of heights attached to principally polarized abelian varieties.
DOI : 10.4153/S0008414X22000220
Mots-clés : Tropical Jacobian, moment, random spanning trees, Voronoi polytope, zonotope, potential theory, tau invariant, heights of abelian varieties, Arakelov invariants 
Jong, Robin de; Shokrieh, Farbod. Tropical moments of tropical Jacobians. Canadian journal of mathematics, Tome 75 (2023) no. 4, pp. 1045-1075. doi: 10.4153/S0008414X22000220
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     title = {Tropical moments of tropical {Jacobians}},
     journal = {Canadian journal of mathematics},
     pages = {1045--1075},
     year = {2023},
     volume = {75},
     number = {4},
     doi = {10.4153/S0008414X22000220},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000220/}
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