The boy's name is Allie, and he is played by actor Chris Parker. Allie is a drifter who spends most of his time wandering around the lower east side of Manhattan, killing time and avoiding responsibility. However, he is deeply passionate about jazz music, especially the works of saxophonist Charlie Parker.
Allie's father is absent, and his mother is in an institution. Allie visits her occasionally but doesn't stay for long. He has no close family members or friends and appears to be emotionally disconnected from everything.
Throughout the film, Allie meets several eccentric characters, including a prostitute named Leila, a young French girl, and a decrepit street artist. Allie spends time with each of them; however, his connection with them is brief and tenuous.
The film is shot in black and white and follows a dreamlike narrative structure. Director Jim Jarmusch cleverly weaves real-life locations in the lower east side of Manhattan with Allie's existential journey.
Overall, Permanent Vacation is an intimate portrayal of a lonely young man searching for identity in a fast-paced, indifferent city. It is a film that, even though it is over thirty years old, still resonates with people today.