Cyclization of a polymer: first-passage problem for a non-Markovian process.

We discuss a closure of a polymer chain released from a state with given end-to-end distance. Considering the situation as a first passage problem for a non-Markovian process, we express the survival probability through the three-time distribution of the end-to-end distance and evaluate it numerically by solving a Volterra equation. We also show how the Wilemski-Fixmann approximation emerges within this scheme and discuss its geometrical nature.