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Monotonicity and phase transition for the edge-reinforced random walk

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If you have a question about this talk, please contact Perla Sousi .

The linearly edge reinforced random walk (ERRW) was introduced in 1986 by Coppersmith and Diaconis and is one of the first example of reinforced random walks. Recently a link has been found between this model, the vertex reinforced jump process and a random spin model. Because of these links it was possible to show that in dimension 3 and above, the ERRW is recurrent for large reinforcement and transient for small ones and thus exhibits a phase transition. We will present the links between those models and show that the model has some monotonicity (the larger the reinforcements the more recurrent it is) and that its phase transition is unique.

This talk is part of the Probability series.

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Discussion Room St Paul's Church, Hills Road, Cambridge, CB2 1JP Concert Hall, Faculty of Music

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