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We consider the Artin groups of dihedral type I 2 (k) defined by the presentation A k = 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 A k with respect to the Artin generators {a, b, a −1 , b −1 } are… (More)

In memory of Daniel Mollier, our former mathematics teacher at the Lycée Louis le Grand, Paris. Consider the braid group B3 = a, b|aba = bab and the nearest neighbor random walk defined by a probability ν with support {a, a −1 , b, b −1 }. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight polynomial… (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)

This paper is an appendix to the paper " Random walks on free products of cyclic groups " by J. Mairesse and F. Mathéus. It contains the details of the computations and the proofs of the results concerning the examples treated there.

In memory of Daniel Mollier, our former mathematics teacher at the Lycée Louis le Grand, Paris. Consider the braid group B 3 = =a, b|aba = bab and the nearest neighbor random walk defined by a probability ν with support {a, a −1 , b, b −1 }. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight… (More)

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