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Discrete Mathematics Seminar


Title: Some asymptotics for connected components of a sparse random graph
Speaker(s): Anatolii Puhalskii
Affiliation: UCD Department of Mathematical and Statistical Sciences
When: Monday,  March 26, 2012
Time: 11:00 AM  -  12:00 PM
Where: CU building, Room 656

A classical result by Erdos-Renyi provides a law of large numbers for the size of the giant component of a sparse random graph. In this talk, I will discuss some related asymptotics which concern the sizes of connected components, their numbers of excess edges, and the number of components.

In particular, conditional laws of large numbers will be presented which establish the existence of additional giant components given that the graph has a number of giant components of certain size. These asymptotics are derived as consequences of the limit behaviour of a certain stochastic process associated with the random graph.



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