D. Aldous, The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees, SIAM Journal on Discrete Mathematics, vol.3, issue.4, pp.450-465, 1990.
DOI : 10.1137/0403039

V. Anantharam and P. Tsoucas, A proof of the Markov chain tree theorem, Statistics and probability letters, pp.189-192, 1989.

A. Broder, Generating random spanning trees, 30th Annual Symposium on Foundations of Computer Science, pp.442-447, 1989.
DOI : 10.1109/SFCS.1989.63516

P. M. Cohn, Free Rings and Their Relations, 1985.

P. M. Cohn, From Hermite rings to Sylvester domains, Proceedings of the American Mathematical Society, vol.128, issue.07, pp.1899-1904, 2000.
DOI : 10.1090/S0002-9939-99-05189-8

P. M. Cohn, Free ideal rings and localization in general rings, 2005.
DOI : 10.1017/CBO9780511542794

M. Fliess, Sur le plongement de l'algèbre des séries rationelles non commutatives dans un corps gauche, pp.926-927, 1970.

I. M. Gelfand and V. Retakh, A theory of noncommutative determinants and characteristic functions of Graphs, I., Publications du LACIM, pp.14-15, 1993.

I. Gelfand and V. Retakh, Determinants of matrices over noncommutative rings, Functional Analysis and Its Applications, vol.51, issue.1, pp.91-102, 1991.
DOI : 10.1007/BF01079588

I. Gelfand and V. Retakh, The theory of noncommutative determinants and characteristic, Funct. Anal. Appl, vol.26, issue.4, pp.1-20, 1992.

I. Gelfand, S. Gelfand, V. Retakh, and R. Wilson, Quasideterminants, Advances in Mathematics, vol.193, issue.1, pp.56-141, 2005.
DOI : 10.1016/j.aim.2004.03.018

T. Lancaster and M. Tismenetsky, Theory of matrices, 1983.

F. T. Leighton and R. L. Rivest, The Markov chain tree theorem, 1983.

L. Lovász and P. Winkler, Exact mixing in an unknown Markov chain, Electronic journal of Combinatorics, issue.2, p.15, 1995.

S. Lavallée, Québecà Montréal E-mail address: lavallee.sylvain.2@courrier.uqam.ca Christophe Reutenauer: Département de mathématiques, Université du Québec Québec`Québecà Montréal E-mail address: reutenauer.christophe@uqam.ca Vladimir Retakh, E-mail address: vretakh@math.rutgers.edu Dominique Perrin: Institut Gaspard-Monge