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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The vertex-reinforced jump process with long-range interactions

## The vertex-reinforced jump process with long-range interactionsAdd to your list(s) Download to your calendar using vCal - Silke Rolles (Technische Universität München)
- Friday 12 July 2024, 10:15-11:15
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. SSDW01 - Self-interacting processes Consider the vertex-reinforced jump process on the complete graph with vertex set Zd, d=1,2,..., and edge weights Wij=w(|i-j|), i,j in Zdwith a strictly positive decreasing weight function w. If w satisfies a summability condition and a suitable lower bound, then the vertex-reinforced jump process is a.s. transient. Using the representation of the discrete time process associated with the vertex-reinforced jump process on finite boxes as a random walk in random conductances, the key estimate consists in a bound for (cosh ui)m for the corresponding H2|2 model. We compare this H2|2 model withanother H2|2 model with hierarchical interactions. The task of studying cosh ui in the last model can be reduced to studying it in an effective H2|2 model on a line graph with inhomogeneous interactions. The proof of some estimates is inspired by work of Disertori-Spencer-Zirnbauer 2010. The talk is based on https://arxiv.org/abs/2305.07359, which is joint work with Margherita Disertori and Franz Merkl. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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