How much notice do we need to give?(M)

[asharding]

We're closing on our new house Oct. 21. There's a chance we might be able to move in on Oct. 31, but we won't know for sure until, well, Oct. 21. In terms of our rental here, we're not on a lease (lovely landlord neglected to send it this year) so I'm assuming we're tenants at will right now. The building is rent stabilized and the last lease we signed ran out Aug, 31; we've signed nothing else since then.

What are our obligations in terms of giving them notice? Can we just say on Oct. 21 that we're moving Oct. 31? We're assuming that our security deposit will cover our last month's rent (and are holding off on paying October rent till we know what's going on).

I have no qualms about inconveniencing our landlord, who has been crappy about keeping up the building and unresponsive in many other ways, but I'm trying to avoid any sort of legal trouble (or us owing them any more $ than we have to!) Can we skip out with such little notice? Thanks in advance!