Local limit theorems for giant components
|
Tue, 30/10/2012 14:30 |
Oliver Riordan (Oxford) |
Combinatorial Theory Seminar  |
SR1 |
| In an Erdős–Rényi random graph above the phase transition, i.e., where there is a giant component, the size of (number of vertices in) this giant component is asymptotically normally distributed, in that its centred and scaled size converges to a normal distribution. This statement does not tell us much about the probability of the giant component having exactly a certain size. In joint work with Béla Bollobás we prove a `local limit theorem' answering this question for hypergraphs; the graph case was settled by Luczak and Łuczak. The proof is based on a `smoothing' technique, deducing the local limit result from the (much easier) `global' central limit theorem. | |||