Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Loop-erased random walks and heaps of cycles

Auteur(s):

Code(s) de Classification MSC:

• 60C05 Combinatorial probability
• 60J15 Random walks

Résumé: We introduce a combinatorial structure, called {\it heap of cycles}, and use it for the study of loop-erased random walks. In particular, we give a pathwise explanation of Wilson's algorithm [7] and of a recent result on random Hamiltonian cycles [5], generalizing Pitman's result on random walks on the circle. The general model of heaps was introduced in combinatorics by Viennot [8].

Mots Clés: loop-erased random walks, occupatiom measure

Date: 1999-11-09

Prépublication numéro: PMA-539