Will property taxes automatically increase after I buy a home in NYC?

[ping]

I know that in California property taxes are essentially frozen at the time of purchase to protect long-time residents from being kicked out of their homes because of unsustainable property tax assessment increases due to gentrification. This means if you're new money, and you buy a home that's been owned and lived in for say 40 years, you're going to pay a heck of a lot more in property tax than the previous owner. That's because California will re-rate and re-assess the property once it trades.

Is there something similar in New York that we should be worried about? Obviously what's listed for monthly taxes is a big factor in our calculations. We don't want to buy a condo in NYC only to immediately face much higher property taxes. We just want to know what we're getting ourselves into.

Thanks!