Supercritical behaviour in random subgraph models
Supercritical behaviour in random subgraph models
Disciplines
Mathematics (100%)
Keywords
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Random graphs,
Probabilistic methods,
Graph Expansion,
Phase transitions
Percolation, or random subgraphs, is a mathematical model originally studied in the context of statistical physics, where they model the flow of a liquid or gas through a lattice like medium whose channels are randomly blocked. For many of these models, as the density of the random subgraph increases, there is a threshold at which its likely structure changes dramatically. Below this threshold all the components are small, whereas above this threshold many of these small component coalesce and a unique large component appears. In this supercritical regime, whilst the random subgraph is still quite sparse and disconnected, its largest component displays many interesting structural properties which you would expect to appear only for much denser graphs. This project aims to investigate the structural properties of these supercritical random subgraphs, and in particular their largest components, in a range of percolation models.
- Technische Universität Graz - 100%
Research Output
- 5 Citations
- 6 Publications
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2024
Title A note on the width of sparse random graphs DOI 10.1002/jgt.23081 Type Journal Article Author Anh T Journal Journal of Graph Theory Pages 273-295 Link Publication -
2024
Title Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs DOI 10.1007/s00493-024-00089-0 Type Journal Article Author Diskin S Journal Combinatorica Pages 741-784 Link Publication -
2023
Title A lower bound for set-coloring Ramsey numbers DOI 10.1002/rsa.21173 Type Journal Article Author Aragão L Journal Random Structures & Algorithms Pages 157-169 Link Publication -
2023
Title Counting orientations of random graphs with no directed k-cycles DOI 10.1002/rsa.21196 Type Journal Article Author Campos M Journal Random Structures & Algorithms Pages 676-691 Link Publication -
2023
Title Ubiquity of graphs with nowhere-linear end structure DOI 10.1002/jgt.22936 Type Journal Article Author Bowler N Journal Journal of Graph Theory Pages 564-598 Link Publication -
2023
Title Isoperimetric stability in lattices DOI 10.1090/proc/16439 Type Journal Article Author Barber B Journal Proceedings of the American Mathematical Society Pages 5021-5029 Link Publication