Geodesic
Spaces of Lorentzian and real stable polynomials are Euclidean balls
Forum of Mathematics, Sigma, Tome 9 (2021)

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We prove that projective spaces of Lorentzian and real stable polynomials are homeomorphic to Euclidean balls. This solves a conjecture of June Huh and the author. The proof utilises and refines a connection between the symmetric exclusion process in interacting particle systems and the geometry of polynomials. 
@article{10_1017_fms_2021_70,
     author = {Petter Br\"and\'en},
     title = {Spaces of {Lorentzian} and real stable polynomials are {Euclidean} balls},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2021.70},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.70/}
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Petter Brändén. Spaces of Lorentzian and real stable polynomials are Euclidean balls. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.70

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