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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)
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)
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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