WASHINGTON — “Let’s go get a steak sometime,” Anthony Scaramucci said, throwing his arm around a reporter who turned up at his West Wing office on Wednesday to make contact with the latest — and most profane, wisecracking, roguishly irrepressible — New Yorker to join President Trump’s staff.

Mr. Scaramucci, widely known by his nickname “the Mooch,” had just become the White House communications director, and he was wasting no time shaking up the joint. By the end of the day, he would tweet that he had asked the F.B.I. to investigate the leaking of a personal financial disclosure form, and all but accused the chief of staff, Reince Priebus, of being the one who had done it. (He finished the night, predictably, with friends at a steakhouse.)

So riveting is the cage match between Mr. Scaramucci and Mr. Priebus that it has elbowed aside even Mr. Trump’s relentless public tormenting of his attorney general, Jeff Sessions. But Mr. Scaramucci’s fiery first week, a brash, blustering performance that at times verged on self-parody, illustrates a deeper truth about the Trump White House: New Yorkers have taken over the West Wing and are turbocharging its culture.

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“The Mooch is a New Yorker like me,” said Rudolph W. Giuliani, the former mayor and an adviser to Mr. Trump who has yet to find his way to a White House job. “He’s a purebred New Yorker. He’s lit a firecracker in that place. What you’re seeing in Scaramucci is the president’s style.”

Mr. Trump has lamented to aides that he cannot visit his apartment in Trump Tower because the security precautions are so costly and would tie up Fifth Avenue and other streets in Midtown Manhattan. So, in some ways, he has simply moved Trump Tower to Pennsylvania Avenue.

Mr. Scaramucci joins a long list of people from the New York metro area who occupy prime real estate near the president: Hope Hicks, Dan Scavino Jr., Keith Schiller, Kellyanne Conway, Gary D. Cohn, Dina Powell, Steven Mnuchin, Wilbur Ross, Jason D. Greenblatt, Michael Anton, Josh Raffel — not to mention Mr. Trump’s daughter Ivanka Trump, and his son-in-law, Jared Kushner.

The vibe, to be sure, is less Manhattan than tristate: Ms. Hicks, Mr. Trump’s discreetly powerful assistant, grew up in Greenwich, Conn. Ms. Conway, his counselor and campaign manager, is from New Jersey; she was born in Camden and lives in Alpine. Mr. Schiller, who was Mr. Trump’s bodyguard and now runs Oval Office operations, was born in the Bronx and grew up in the Hudson Valley. Mr. Scaramucci, who is 53, was raised on Long Island.

“Jared is New Jersey — that’s close enough,” Mr. Giuliani said of Mr. Kushner, who was born in Livingston.

A few of the New Yorkers are transplants: Ms. Powell was born in Cairo and moved to Texas and Washington before ending up in Manhattan at Goldman Sachs. Mr. Cohn, who rose to the No. 2 job at Goldman Sachs, is originally from Shaker Heights, Ohio. But even the transplants sometimes behave as if they, and their boss, never left the five boroughs.

When Mr. Cohn, the president’s chief economic adviser, briefed reporters at a summit meeting in Sicily in May, he boasted that Mr. Trump had been working nonstop since leaving New York a few days earlier.

“Washington,” the national security adviser, Lt. Gen. H .R. McMaster, leaned in to correct him.

Presidents often bring a retinue from their home states that gives the White House a distinct cultural accent — often to the disdain of Washington’s permanent establishment. Jimmy Carter’s young aides were quickly labeled the “Georgia Mafia.” Richard M. Nixon and Ronald Reagan each came with a powerful, not always popular, California contingent.

The closest analogy to Mr. Trump’s White House was Franklin D. Roosevelt’s. A former governor of New York, Roosevelt populated his administration with Columbia University professors and influential New Yorkers like Henry Morgenthau Jr., who was his Treasury secretary.

“How much it changes things depends a great deal on how experienced they are with Washington politics,” said Robert Dallek, the presidential historian, who will publish a new biography of Roosevelt this fall. “There is a Washington culture that often surpasses what they may have brought with them from Georgia or Texas or New York.”

As much as Mr. Trump’s New York contingent has set the tone in the West Wing, its influence on the administration’s policy has been, at best, mixed. Mr. Cohn, along with Mr. Kushner and Ms. Trump, failed to talk the president out of withdrawing from the Paris climate accord. They have not appreciably softened his policies on trade or immigration.

Mr. Trump’s speeches and policies still bear the unmistakable imprint of his senior policy adviser, Stephen Miller, and his chief strategist, Stephen K. Bannon. Both are ardent nationalists who are scathing about the mainstream tendencies of the New York crowd — and neither is a New Yorker. Mr. Miller grew up in Santa Monica, Calif.; Mr. Bannon was born in Norfolk, Va., though he lived in New York when he worked for Goldman Sachs.

Mr. Scaramucci’s stormy debut has not impressed old Washington hands. Some predict that the capital will chew him up the way it did his headstrong predecessors. Others were stunned by an interview he gave The New Yorker, in which he threatened bodily harm and flung lewd epithets at senior White House officials, whom he accused of leaking to reporters.

“Scaramucci’s full of himself,” Newt Gingrich, a former House speaker, said on CNN on Thursday. “I think he got down here from New York. I think he’s all excited. And I think he’s frankly talking more than he’s thinking. He needs to slow down and learn the business.”

Hank Sheinkopf, a longtime New York political consultant, said: “These New Yorkers believe they can imprint New York and its streets on a city that hates confrontation and exposure. Washington is a place where a meeting is seen as an accomplishment. New York is a place where a fistfight is seen as an outcome.”

Mr. Scaramucci seems aware of the danger. He is turning away requests for profile pieces, and he has told aides that he wants to make changes to give the White House communications operation a better relationship with the news media (though he vowed on Thursday night never to trust reporters again). There is little doubt that he is operating with the president’s wholehearted approval.

Mr. Giuliani said that Mr. Scaramucci embodied the president’s “intensity and can-do spirit.” It will be a valuable trait, he said, in a city that is built to resist change. Mr. Giuliani noted that the New Yorkers in Mr. Trump’s administration were not chosen because of political patronage or party loyalty. Mr. Cohn is a Democrat. Mr. Scaramucci has tweeted nice things about former President Barack Obama, who was a few years behind Mr. Scaramucci at Harvard Law School.

Beyond their qualifications, Mr. Trump appears to relish the swagger and in-your-face approach of fellow New Yorkers. Far from discouraging conflict, he seems to foment it. Mr. Scaramucci posted his incendiary tweet about Mr. Priebus — now deleted — after he had dinner at the White House with Mr. Trump and another bluff New Yorker, the Fox News host Sean Hannity.

“Trump connects to other New Yorkers,” said Christopher Ruddy, chief executive of Newsmax Media and a friend of the president. “He calls these people killers, and that’s the ultimate compliment. You tell it like it is, you let it hang out, you can be a little nasty with each other.”

And what about non-New Yorkers, like Mr. Priebus, who was born in New Jersey but grew up in Wisconsin?

“They need to go to lessons in New York attitude and behavior,” said Mr. Ruddy, who, like Mr. Scaramucci, grew up on Long Island.