Scaling limits and local weak limits of random structures
Final Report Abstract
In this project we made important contributions to the universality class of the Brownian continuum random tree and constructed novel infinite random graphs that describe the asymptotic local behaviour of random discrete structures. We treated classical probabilistic models such as Galton-Watson trees conditioned to be large and combinatorial models such as weighted random graphs from restricted classes. This advances our understanding of how random structures behave on a global and local scale. In the process we developed tools describing a congelation phenomenon in random set partitions. These turned out to be interesting in their own right and allowed us to recover and greatly generalize classical results on the structure of connected components in addable minor-closed classes of graphs.
Publications
- Asymptotic properties of random unlabelled block-weighted graphs
B. Stufler
- Graph limits of random graphs from a subset of of connected k-trees
M. Drmota, E. Y. Jin, B. Stufler
- Graph limits of random unlabelled k-trees
E. Y. Jin, B. Stufler
- Gibbs partitions: the convergent case. Random Structures & Algorithms
B. Stufler
- Local limits of large Galton-Watson trees rerooted at a random vertex. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
B. Stufler
