Tropical Geometry

Topics

Incentive Compatible Mechanisms

Bo Lin and Ngoc Mai Tran applied results in tropical geometry to the study of mechanism design (Two-player incentive compatible mechanisms are affine maximizers). They proved that for two-player games on a discrete type space, any given mechanism can be turned into an affine maximizer through a nontrivial perturbation of the type space. In their proof, they connected the incentive compatible mechanisms of a type space T to the tropical determinant of the minors of the matrix T.

Zeros of Random Tropical Polynomials

Ngoc Mai Tran and François Baccelli derived a tropical version of the result of Kac on the zeros of polynomials with random coefficients (Zeros of Random Tropical Polynomials, Random Polygons and Stick-Breaking). 

The common roots of tropical of a class of random polynomials in two variables is analyzed in a recent work by the same authors in Iterated Gilbert Mosaics and Poisson Tropical Plane Curves using a stochastic geometry approach based on iterated random tessellations.

Members

Bo Lin

Department of Mathematics, UT Austin
bolin@math.utexas.edu
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Ngoc Mai Tran

Department of Mathematics, UT Austin
ntran@math.utexas.edu
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François Baccelli

Department of Mathematics and Deparment of Electrical and Computer Engineering, UT Austin
baccelli@math.utexas.edu
512 471 17 54
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Publications

2017-10-18_1001064

Two-player incentive compatible mechanisms are affine maximizers

Bo Lin and Ngoc Mai Tran https://arxiv.org/abs/1710.05218
2016-10-16_1000749

Iterated Gilbert Mosaics and Poisson Tropical Plane Curves

Francois Baccelli and Ngoc Tran https://arxiv.org/abs/1610.08533
2015-09-13_1000135

Zeros of Random Tropical Polynomials, Random Polygons and Stick-Breaking

François Baccelli and Ngoc Mai Tran To appear in the Transctions of the AMS 2015
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