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Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique

Sandrine Roussel (2000)

Colloquium Mathematicae

The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let Q * k denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value k n for which the total variation norm between Q * k and π stays very close to 1 for k k n , and falls rapidly to a value close to 0 for k k n with a fall-off phase much shorter than k n . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...

Poisson boundary of triangular matrices in a number field

Bruno Schapira (2009)

Annales de l’institut Fourier

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.

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