Random graph models for real-world networks
Department Away Day `24
Joost Jorritsma
Math,
Music,
Biking
Understanding network models
Probability, Combinatorics
& Physics, Epidemiology, ...
Information diffusion in random graphs
Distances
Component sizes
Intervention strategies
FINAL SIZE
Randomized optimization algorithms
Optimization under chance constraints
Sampling algorithms for explainable AI
Inhomogeneous degrees, triangles, and small world
Inhomogeneous degrees, triangles, and small world
Inhomogeneous degrees, triangles, and small world
Inhomogeneous degrees, triangles, and small world
Vertex set
- Spatial locations
- Vertex weights
Edge more likely if
- Spatially nearby,
- High weight
Spatial random graphs
Percolation: Reed-Frost epidemic
Four parameters: new and classical models
New phenomena
- Delocalized connected components
- Double-exponential neighbourhood growth
- Large outbreaks more likely than small outbreaks
Challenges
- Geometry:
- Short/Long edges
- Presence of hubs
New direction: Scaling limits of trees and random graphs
- Only vertex weights, no location
- Edge lengths scale with graph size
Figure by Igor Kortchemski
Setup
- Include asymmetry in edge probabilities
- Uncountable and unbounded weights
Goal
References
- The Continuum Random Tree; David Aldous; Annals of Probability (1991).
-
Limits of multiplicative inhomogeneous random graphs and Lévy trees: limit theorems;
Nicolas Broutin, Thomas Duquesne, Minmin Wang; Probability Theory & Related Fields (2021). -
Cluster-size decay in supercritical long-range percolation;
With Júlia Komjáthy, Dieter Mitsche; Electronic Journal of Probability (2024). -
Cluster-size decay in supercritical kernel-based spatial random graphs;
With Júlia Komjáthy, Dieter Mitsche; Min. revision in Annals of Probability, arXiv: 2303.00712. -
Large deviations of the giant in supercritical kernel-based spatial random graphs;
With Júlia Komjáthy, Dieter Mitsche; Preprint arXiv: 2404.02984. -
Surface order large deviations for Ising, Potts and percolation models;
Agoston Pisztora; Probability Theory and Related Fields (2024).
Department Away Day `24
Joost Jorritsma
Random graph models for real-world networks
Department Away Day `24
Joost Jorritsma