  We consider eukaryotic DNA replication and in particular the role of
replication origins in this process. We focus on origins which are `active' -
that is, trigger themselves in the process before being read by the replication
forks of other origins. We initially consider the spacings of these active
replication origins in comparison to certain probability distributions of
spacings taken from random matrix theory. We see how the spacings between
neighbouring eigenvalues from certain collections of random matrices has some
potential for modelling the spacing between active origins. This suitability
can be further augmented with the use of uniform thinning which acts as a
continuous deformation between correlated eigenvalue spacings and exponential
(Poissonian) spacings. We model the process as a modified 2D Poisson process
with an added exclusion rule to identify active points based on their position
on the chromosome and trigger time relative to other origins. We see how this
can be reduced to a stochastic geometry problem and show analytically that two
active origins are unlikely to be close together, regardless of how many
non-active points are between them. In particular, we see how these active
origins repel linearly. We then see how data from various DNA datasets match
with simulations from our model. We see that whilst there is variety in the DNA
data, comparing the data with the model provides insight into the replication
origin distribution of various organisms.
