Séminaire de Probabilités commun ICJ/UMPA

Monotonicity and phase transition for the linearly edge-reinforced random walk

by Rémy Poudevigne

BBB (En ligne)


En ligne


We will present two models of reinforced random walks: the linearly edge-reinforced random walk (ERRW), the vertex reinforced Jump Process(VRJP) and how the two models are linked. Both models depends on initial weights, on some graphs they can be recurrent for small weights and transient for large ones. We will show that when we decrease the initial weights both models get more recurrent in a certain sense. This in turns means that both models exhibit a phase transition in dimensions 3 and more: they are recurrent up until some critical weight after which they are transient.


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