In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Rényi random graph G(n, p), where p∈(0,1) is a fixed constant. Our proof is based on bounding the characteristic function ψ(t) of the number of triangles, and uses several different conditioning arguments for handling different ranges of t.
All Science Journal Classification (ASJC) codes
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Characteristic function
- Local limit theorem
- Random Graphs
- Subgraph counts