The distribution of the number of academic publications as a function of citation count for a given year is remarkably similar from year to year. We measure this similarity as a width of the distribution and find it to be approximately constant from year to year. We show that simple citation models fail to capture this behaviour. We then provide a simple three parameter citation network model using a mixture of local and global search processes which can reproduce the correct distribution over time. We use the citation network of papers from the hep-th section of arXiv to test our model. For this data, around 20% of citations use global information to reference recently published papers, while the remaining 80% are found using local searches. We note that this is consistent with other studies though our motivation is very different from previous work. Finally, we also find that the fluctuations in the size of an academic publication’s bibliography is important for the model. This is not addressed in most models and needs further work.