Restrictions of some reinforced processes to subgraphs
Abstract
We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes.A similar statement holds for the non-linear hyperbolic supersymmetric sigma model.This is then applied to vertex-reinforced jump processes on subdivided versions of graphs of bounded degree, where every edge is replaced by a sufficiently large finite sequence of edges.We prove that discrete-time processes associated to suitable corresponding restrictions are mixtures of positive recurrent Markov chains.As a consequence, we also obtain that the vertex-reinforced jump process on these subdivided graphs is recurrent.We also deduce a similar statement for edge-reinforced random walks.
Fields of Study & Subjects
Mathematical Approximation and Integration
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 2
- Pages
- 1077–1077
- Publication date
- 1 January 2026
- Language
- EN