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- Jean Mairesse, Frédéric Mathéus
- IJAC
- 2006

We consider the Artin groups of dihedral type I2(k) defined by the presentation Ak = 〈a, b | prod(a, b; k) = prod(b, a; k)〉 where prod(s, t; k) = ststs..., with k terms in the product on the right-hand side. We prove that the spherical growth series and the geodesic growth series of Ak with respect to the Artin generators {a, b, a, b−1} are rational. We… (More)

Consider the braid group B3 = 〈a, b|aba = bab〉 and the nearest neighbor random walk defined by a probability ν with support {a,a, b, b}. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight polynomial equations of degree three over eight indeterminates. We also explicitly describe the harmonic measure… (More)

- SÉBASTIEN GOUËZEL, Frédéric Mathéus, FRANÇOIS MAUCOURANT
- 2012

The entropy, the spectral radius and the drift are important numerical quantities associated to any random walk with finite second moment on a countable group. We prove an optimal inequality relating those quantities, improving upon previous results of Avez, Varopoulos, Carne, Ledrappier. We also deduce inequalities between these quantities and the volume… (More)

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