Seminar series
Date
Tue, 30 Oct 2012
Time
14:30 -
15:30
Location
SR1
Speaker
Oliver Riordan
Organisation
Oxford
In an Erdős--R\'enyi 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 B\'ela
Bollob\'as 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.