  Cell division times in microbial populations display significant
fluctuations, that impact the population growth rate in a non-trivial way. If
fluctuations are uncorrelated among different cells, the population growth rate
is predicted by the Euler-Lotka equation, which is a classic result in
mathematical biology. However, cell division times can be significantly
correlated, due to physical properties of cells that are passed through
generations. In this paper, we derive an equation remarkably similar to the
Euler-Lotka equation which is valid in the presence of correlations. Our exact
result is based on large deviation theory and does not require particularly
strong assumptions on the underlying dynamics. We apply our theory to a
phenomenological model of bacterial cell division in E.coli and to experimental
data. We find that the discrepancy between the growth rate predicted by the
Euler-Lotka equation and our generalized version is relatively small, but large
enough to be measurable by our approach.
