Is it permissible to use hot tap water on Shabbat if you are living in a large building which has a majority of non-Jewish tenants? I have heard the argument that since there will be many other people using the water at one time, you will not be causing water to be heated? What is the Halacha L’maaseh?

I'm not sure I understand the question - What does the fact it's a big building have to do with the heating of the water? If you have a private water heating system – of course you can't use the hot water tap. If the building has a general water heating system for the whole building – I can hear the argument – yet I still think you should not use it since it still has an effect on the cold water that will heat up on Shabbat.