Biane, Philippe Marches de Bernoulli quantiques. (Quantum Bernoulli walks). (French) Zbl 0701.60103 Séminaire de probabilités XXIV 1988/89, Lect. Notes Math. 1426, 329-344 (1990). [For the entire collection see Zbl 0695.00024.] We study a quantum analogue of the classical Bernoulli random walk: instead of one Bernoulli random variable, one considers three noncommuting random variables, which can be represented by Pauli matrices; then one adds independent copies of these: three quantum random variables, obtaining three non-commuting Bernoulli random walks. Using the representation theory of the Lie algebra SU(2), one derives several probabilistic results on these quantum stochastic processes. In particular, the “Euclidean norm” of this process is shown to be Markovian, and the transition probabilities are computed using Clebsch- Gordan formulae. Reviewer: Ph.Biane Cited in 1 ReviewCited in 1 Document MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G50 Sums of independent random variables; random walks Keywords:quantum probability; non-commuting Bernoulli random walks; Clebsch-Gordan formulae Citations:Zbl 0695.00024 PDFBibTeX XML Full Text: Numdam EuDML