COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model (II)

## Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model (II)Add to your list(s) Download to your calendar using vCal - Tarres, P (University of Oxford)
- Wednesday 19 September 2012, 09:30-10:10
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. This talk has been canceled/deleted 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. Then we prove that the VRJP is a mixture of time-changed Markov jump processes and calculate the mixing measure, which we interpret as a marginal of the supersymmetric hyperbolic sigma model introduced by Disertori, Spencer and Zirnbauer. This enables us to deduce that VRJP and ERRW are strongly recurrent in any dimension for large reinforcement (in fact, on graphs of bounded degree), using a localisation result of Disertori and Spencer (2010). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
## Other listsDepartment of Engineering, Production Processes Group Seminars, Institute for Manufacturing Carving object representation at itâ€™s multi-level joints Hitachi Cambridge Seminar Series## Other talksCoin Betting for Backprop without Learning Rates and More Polynomial approximation of high-dimensional functions on irregular domains Climate change, species' abundance changes and protected areas Poison trials, panaceas and proof: debates about testing and testimony in early modern European medicine First order rigidity of higher rank arithmetic lattices (note the nonstandard day) Symplectic topology of K3 surfaces via mirror symmetry Stromal microenvironments and the control T-cell development and selection The Rise of Augmented Intelligence in Edge Networks Atiyah Floer conjecture Computing High Resolution Health(care) Current-Induced Stresses in Ceramic Lithium-Ion Conductors |