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SUMMARY:The vertex-reinforced jump process with long-range interactions - 
 Silke Rolles (Technische Universität München)
DTSTART:20240712T091500Z
DTEND:20240712T101500Z
UID:TALK215611@talks.cam.ac.uk
DESCRIPTION:Consider the vertex-reinforced jump process on the complete gr
 aph with vertex set Zd\, d=1\,2\,...\,&nbsp\; 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 ve
 rtex-reinforced jump process is a.s. transient.\nUsing the representation 
 of the discrete time process associated with the vertex-reinforced jump pr
 ocess on finite boxes as a random walk in random conductances\, the key es
 timate 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 inte
 ractions. 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 Disertor
 i-Spencer-Zirnbauer 2010.&nbsp\;\nThe talk is based on https://arxiv.org/a
 bs/2305.07359\, which is joint work with Margherita Disertori and Franz Me
 rkl.
LOCATION:Seminar Room 1\, Newton Institute
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