Mathematics – Probability
Scientific paper
2011-11-16
Mathematics
Probability
Minor improvements; we provide a self-contained proof of our adaptation of Disertori and Spencer's localization result (2010)
Scientific paper
Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986, is a random process, which takes values in the vertex set of a graph G, and is more likely to cross edges it has visited before. We show that it can be represented in terms of a Vertex-reinforced jump process (VRJP) with independent gamma conductances: the VRJP was conceived by Werner and first studied by Davis and Volkov (2002,2004), and is a continuous-time process favouring sites with more local time. We calculate, for any finite graph G, the limiting measure of the centred occupation time measure of VRJP, and interpret it as a supersymmetric hyperbolic sigma model in quantum field theory. This enables us to deduce that VRJP and ERRW are strongly recurrent in any dimension for large reinforcement, using a localisation result of Disertori and Spencer (2010).
Sabot Christophe
Tarres Pierre
No associations
LandOfFree
Edge-reinforced random walk, Vertex-Reinforced Jump Process and the supersymmetric hyperbolic sigma model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Edge-reinforced random walk, Vertex-Reinforced Jump Process and the supersymmetric hyperbolic sigma model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Edge-reinforced random walk, Vertex-Reinforced Jump Process and the supersymmetric hyperbolic sigma model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-349069