A woman with no prior relationship with a well-known local celebrity becomes utterly convinced he is secretly in love with her and has been sending her coded signals through his public appearances. When he makes no contact, she concludes his letters must be being intercepted. What is this?

This is a delusion of love: a fixed conviction that another person, here with essentially no real relationship to her, is secretly in love with her, complete with the distinctive and clinically useful feature of explaining away the absence of any reciprocal contact (intercepted letters) rather than treating it as evidence against the belief. It is not ordinary infatuation, which does not carry this fixed, unshakeable conviction that the feeling is mutual and secretly known to be so. It is not a delusion of persecution, since the content here is about being loved, not harmed. And no belief about another person's identity being altered is described, so this is not a delusion of misidentification.