Résumé
I give a review of some rigorous results on self avoiding walks in cubic and hypercubic lattices, including the case of self-avoiding Levy walks. I then explain the connection with supersymmetric field theory and go on to give an exposition of rigorous renormalization group analysis of the supersymmetric measure in the particular case of self avoiding Levy walks below the critical dimension. The talk is based on my joint work with D. Brydges and G. Guadagni (J.Stat.Phys. 115, 415-449 (2004), further work with D.Brydges (2011, in preparation) on finite range multiscale expansions. The renormalization group analysis of the supersymmetric measure based on the above expansions is carried out in joint work with B. Scoppola (J.Stat.Phys. 133, 921-1011 (2008)).