. Nous-venons-ainsi-de-découvrir, une variable aléatoire et celle d'un front se propageant en une dimension selon l'´ equation KPP En fait ií etait déja apparu une connection similaire, qui comme nous allons le voir n'est pasétrangèrèpasétrangèrè a la nôtre : enétudiantenétudiant le modèle d'un polymère dirigé en présence d'´ energies aléatoires sur un arbre de Cayley, Derrida et Spohn avaient remarqué un lien entre la loi de distribution de l'´ energie libre de ce polymère et les solutions de l'´ equation KPP (Derrida & Spohn 1988) Afin d'approfondir un peu tous ces liens, nous allons nous concentrer maintenant sur le modèle que nous avons déjà rencontré initialement : celui d'un seul vortex dans le modèle XY. De façon plus générale, nous allons considérer leprobì eme d'une particule (un vortex) en dimension d, dans un potentiel désordonné. En fonction du type de corrélation de ce potentiel, la physique est différente : du cas décorrélé décrit par le REM, aux corrélations linéaires (modèle de Sinai) en passant par les corrélations logarithmiques qui nous intéressent ici. Notre intérêt essentiel se portera bien sûr sur le cas des corrélations logarithmiques en dimension deux. Nous verrons qu'audeì a du contexte précédent, ce modèle est relié aux propriétés de localisation de la fonction d'onde critique d'un fermion de Dirac bidimensionnel dans un champ magnétique aléatoire. La technique précédente peutégalementêtrepeutégalementpeutégalementêtre 7. Wim Van Saarloos

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