Probabilistic Models on Combinatorial Structures
Statistical mechanics of disordered systems and random combinatorial structures.
Probabilistic Models on Combinatorial Structures. Statistical mechanics of disordered systems and random combinatorial structures.
Foundations and canonical references
The standard treatments of probabilistic models on combinatorial structures approach the subject from complementary angles. Vanderhofstad, Random Graphs and Complex Networks (2017) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for probabilistic models on combinatorial structures include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2017Random Graphs and Complex Networksvanderhofstad-2017
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Percolation
Bernoulli percolation, critical exponents, and SLE connections.
- 02
Schramm–Loewner Evolution
Conformally invariant scaling limits of planar processes.
- 03
Random Trees and Maps
Continuum random tree, Brownian map, and Liouville quantum gravity.
- 04
Spin Glass Theory
Sherrington–Kirkpatrick model, Parisi formula, and replica symmetry breaking.
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