Neighbor will be receiving notice to quit soon?

Since I've moved in she's done nothing but disturb the peace in my household along with her unruly child and company. I've complained so much she's now receiving a notice to quit letter. Based on what management told me is that she'll be given a letter with a date on it. That's all I know. I live in New Jersey. Can someone explain in detail what happens next? The process in detail? Thanks!

Neighbor will be receiving notice to quit soon?
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