Growing influence? In NYC? I really don't think so. They made a lot of noise in the 90's, but nowadays Russian mob activity in NYC, although still existent, seems to be on the more dormant side of the equation.

The most recent two busts involving "Russian" (post-Soviet) organized crime were the Shulaya group in 2017 - which were mostly Georgian gangsters - and the Tsvetkov-Gershman group in 2016 - which were mostly Jewish and Slavic gangsters from Russia, Ukraine, Belarus and Moldova. Both cases involved theft, extortion, gambling, fraud and narcotics. Not really on an unseen scale and nothing that you wouldn't find the local Cosa Nostra crew being involved in, EXCEPT for the almost frightening extortion the Tsvetkov-Gershman group committed. They were literally following relatives of their shakedown victims throughout the USA, Israel and Eastern Europe. Some scary shit.

Their perceived violence is a bit overstated. Except for the inhuman massacres happening in the Mexican cartel world, any criminal group can be as violent and brutal as the other when they need to be. With the "Russians" there isn't really much of an organization as there is with the Italians. They're slightly smaller crews of sorta sophisticated thugs that can turn on each other as quick as they work together. There were lots of whackings in 90's Brighton Beach, but it only concerned other Russian gangsters. They rarely stepped on the toes of other criminal organizations in the city and kept to their own territory.