TALK by J. Schweinsberg
### February 14, 2008

### A waiting time problem arising from the study of
multi-stage carcinogenesis

#### Jason Schweinsberg (UCSD)

We consider a model of a population of fixed
size N in which each individual gets replaced at rate one
and each individual experiences a mutation at rate u.
We calculate the asymptotic distribution of the time
that it takes before there is an individual in the
population with m mutations. A variety of different
behaviors are possible, depending on how u changes with N.
These results have applications to the problem of
determining the waiting time for regulatory sequences
to appear and to models of cancer development. This
talk is partly based on joint work with Rick Durrett
and Deena Schmidt.