## English

• 2015, Thierry Giordano, David Handelman, Radu B. Munteanu, “Nonsingular transformations and dimension spaces”, in arXiv[1]:
For any adic transformation ${\displaystyle T}$ defined on the path space ${\displaystyle X}$ of an ordered Bratteli diagram, endowed with a Markov measure ${\displaystyle \mu }$, we construct an explicit dimension space (which corresponds to a matrix values random walk on ${\displaystyle \mathbb {Z} }$) whose Poisson boundary can be identified as a ${\displaystyle \mathbb {Z} }$-space with the dynamical system ${\displaystyle (X,\mu ,T)}$.