The closed feedback loop in recommender systems is a common setting that can lead to different types of biases. Several studies have dealt with these biases by designing methods to mitigate their effect on the recommendations. However, most existing studies do not consider the iterative behavior of the system where the closed feedback loop plays a crucial role in incorporating different biases into several parts of the recommendation steps. We present a theoretical framework to model the asymptotic evolution of the different components of a recommender system operating within a feedback loop setting, and derive theoretical bounds and convergence properties on quantifiable measures of the user discovery and blind spots. We also validate our theoretical findings empirically using a real-life dataset and empirically test the efficiency of a basic exploration strategy within our theoretical framework. Our findings lay the theoretical basis for quantifying the effect of feedback loops and for designing Artificial Intelligence and machine learning algorithms that explicitly incorporate the iterative nature of feedback loops in the machine learning and recommendation process.