G. N. Arzhantseva and A. Yu, Ol'shanski? ?. Generality of the class of groups in which subgroups with a lesser number of generators are free, pp.489-496, 1996.

F. Bassino, A. Martino, C. Nicaud, E. Ventura, and P. Weil, Statistical properties of subgroups of free groups, Random Structures & Algorithms, vol.16, issue.3, pp.349-373, 2013.
DOI : 10.1002/rsa.20407
URL : https://hal.archives-ouvertes.fr/hal-00450218

F. Bassino, C. Nicaud, and P. Weil, RANDOM GENERATION OF FINITELY GENERATED SUBGROUPS OF A FREE GROUP, International Journal of Algebra and Computation, vol.18, issue.02, pp.375-405, 2008.
DOI : 10.1142/S0218196708004482
URL : https://hal.archives-ouvertes.fr/hal-00164584

F. Bassino, C. Nicaud, and P. Weil, Generic properties of random subgroups of a free group for general distributions, 23rd Intern. Meeting on the Analysis of Algorithms, Discrete Math. Theor. Comput. Sci. Proc., AQ, pp.155-166, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00687981

W. Feller, An introduction to probability theory and its applications, 1968.

. Ph, R. Flajolet, and . Sedgewick, Analytic combinatorics, 2009.

S. M. Gersten, On Whitehead's algorithm, Bulletin of the American Mathematical Society, vol.10, issue.2, pp.281-284, 1984.
DOI : 10.1090/S0273-0979-1984-15246-7

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1214/aoms/1177730491

T. Jitsukawa, Malnormal subgroups of free groups, Computational and statistical group theory, pp.83-95, 2002.
DOI : 10.1090/conm/298/05115

I. Kapovich, A. Miasnikov, P. Schupp, and V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, Journal of Algebra, vol.264, issue.2, pp.665-694, 2003.
DOI : 10.1016/S0021-8693(03)00167-4

I. Kapovich, P. Schupp, and V. Shpilrain, Generic properties of Whitehead???s algorithm and isomorphism rigidity of random one-relator groups, Pacific Journal of Mathematics, vol.223, issue.1, pp.113-140, 2006.
DOI : 10.2140/pjm.2006.223.113

P. Lezaud, Chernoff-type bound for finite Markov chains, The Annals of Applied Probability, vol.8, issue.3, pp.849-867, 1998.
DOI : 10.1214/aoap/1028903453
URL : https://hal.archives-ouvertes.fr/hal-00940907

R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 1977.
DOI : 10.1007/978-3-642-61896-3

A. D. Miasnikov and A. G. Myasnikov, Whitehead method and genetic algorithms, Computational and experimental group theory, pp.89-114, 2004.
DOI : 10.1090/conm/349/06359

Y. Ollivier, invitation to random groups, Soc. Bras. de Matemática, 2005.

A. Roig, E. Ventura, and P. Weil, ON THE COMPLEXITY OF THE WHITEHEAD MINIMIZATION PROBLEM, International Journal of Algebra and Computation, vol.17, issue.08, pp.1611-1634, 2007.
DOI : 10.1142/S0218196707004244
URL : https://hal.archives-ouvertes.fr/hal-00092416

W. Rudin, Real and complex analysis, 1987.

J. Serre, English translation: Trees, Soc. Math. France, 1977.

J. R. Stallings, Topology of finite graphs, Inventiones Mathematicae, vol.4, issue.3, pp.551-565, 1983.
DOI : 10.1007/BF02095993

N. W. Touikan, A FAST ALGORITHM FOR STALLINGS' FOLDING PROCESS, International Journal of Algebra and Computation, vol.16, issue.06, pp.1031-1045, 2006.
DOI : 10.1142/S0218196706003396