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Genus 3 normal coverings of the Riemann sphere branched over 4 points.

Yolanda Fuertes, Manfred Streit (2006)

Revista Matemática Iberoamericana

In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.

Geometric characterization for affine mappings and Teichmüller mappings

Zhiguo Chen (2003)

Studia Mathematica

We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.

Green functions for killed random walks in the Weyl chamber of Sp(4)

Kilian Raschel (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...

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