334 citations · 2.6k across the 129 of their papers we have counts for
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Stationary solutions of discrete and continuous Petri nets with priorities
Xavier Allamigeon, Vianney Boeuf, Stéphane Gaubert
We study a continuous dynamics for a class of Petri nets which allows the routing at non-free choice places to be determined by priorities rules. We show that this dynamics can be…
A tropical isoperimetric inequality
Jules Depersin, Stéphane Gaubert, Michael Joswig
We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is element…
Generic uniqueness of the bias vector of finite stochastic games with perfect information
Marianne Akian, Stéphane Gaubert, Antoine Hochart
Mean-payoff zero-sum stochastic games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair s…
Tropical spectrahedra
Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra
We introduce tropical spectrahedra, defined as the images by the nonarchimedean valuation of spectrahedra over the field of real Puiseux series. We provide an explicit polyhedral c…
Tropical totally positive matrices
Stéphane Gaubert, Adi Niv
We investigate the tropical analogues of totally positive and totally nonnegative matrices. These arise when considering the images by the nonarchimedean valuation of the correspon…
Minimax representation of nonexpansive functions and application to zero-sum recursive games
Marianne Akian, Stéphane Gaubert, Antoine Hochart
We show that a real-valued function on a topological vector space is positively homogeneous of degree one and nonexpansive with respect to a weak Minkowski norm if and only if it c…