I think this will help answer why A.J. and Nic lived on Alice Island, and why he did not move soon after her death.
"Strangely enough, Nic's death had had the opposite effect on business. Though he had opened and closed the store with the emotionless regularity of an SS officer, the fiscal quarter after her death had posted the worst sales in Island's history. Of course, people had felt sorry for him then, but they had felt too sorry for him. Nic had been a local, one of their own. They had been touched when the Princeton graduate (and Alice Island High School salutatorian no less) had returned to Alice to open a bookstore. with her serious-eyed husband. pg. 44
"Copies sell for upward of four hundred thousand dollars depending on condition and the mood of the rare books market. I was planning to auction it off in a couple of years when the economy had had a little time to improve. I was planning to close the shop and retire on the proceeds." pg. 31
So as you can see, Nic wanted to return to her small hometown to open the bookstore, he was from New Jersey. After her death he was in a bit of a zombie state, and we know he was drinking heavily to the point of having black outs. From what we I can gather he did not plan to stay on Alice Island forever.
One last thought before I go on to read chapter 4. I can't help but wonder about the fact Lambiase asks A.J. on pg. 33
"One last thing, I'm wondering who knew about the book?" A.J. snorts. "Everyone. My wife's sister, Ismay teaches at the high school. She worries about me since Nic... She's always bugging me to get out of the store, get off the island. About a year ago, she dragged me to this dreary estate sale in Milton. It was sitting in a box with about fifty other books, all worthless except Tamerlane."
Hmmmm.....Ismay was with A.J. when he found the book, the person who stole the book cleaned up his mess in the kitchen, Ismay wants him to get off the island, Ismay comes to help with Maya and washes the dishes even though he says to leave them. Pg. 55 Ismay knows her husband is cheating on her, and she also knows A.J. knows it, and after she has a miscarriage she tries to kiss A.J. at the hospital. She said, " Nic was the good girl. I'm bad. I married a bad man, too. And I know that bad people deserve what they get, but oh, how we hate to be alone." pg. 78
Is it a far stretch to wonder if she is in love with A.J., and could she have stolen Tamerlane? Is the obvious in front of our eyes? Okay on to chapter 4.