An ombudsman (or ombudsperson as U of Iowa calls it) is someone who helps with conflict resolution. More specifically, here's a quote, although it's from the U of Iowa website because I couldn't find the ombudsman upon quick check of the NYU site:
WELCOME
to The University of Iowa Ombudsperson's Office. The office offers informal dispute resolution for students, faculty and staff. Our mission is to see that all members of the University community are treated fairly. However, we see ourselves as much more than a complaint office; we serve as an information resource as well. The office provides a confidential, safe place to discuss any concerns you might have about the University or its policies or procedures, and we will direct you to the appropriate office for answers to your concerns. This web page will answer some general questions about the Ombud's Office and provide other resources for your perusal. We hope you will explore the various sections of the web page and that you find this information helpful.
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I was just checking out the NYU website, and I found this link that you might want to check out:
http://www.nyu.edu/housing/residencelife/roommates.html
There is information on that page about mediation and arbitration, either of which might be helpful to you. If you are going to prepare for eventual arbitration, you should document, document, document EVERYTHING inappropriate that Paula does -- dates, times, witnesses, any proof at all to back up your side. Maybe you could keep a log on your password protected computer.
Good luck, and keep us posted! I'm sorry you have to deal with this when you should be enjoying the start of a new school year.