OCEANSIDE, Calif. — Gam Aung, a Burmese refugee, had never heard of sushi before arriving in the United States three years ago. Today, he makes six figures a year hawking creations like the Dazzling Dragon roll and the Mango Tango.

Over two years, Mr. Aung, who never finished high school and is still working on his English, went from running one grocery-store sushi counter to three. Along the way, he saved enough for a $700,000 house and trained 10 fellow Burmese to follow in his footsteps.

“I came true with my American dream,” said Mr. Aung, 38, standing behind his sushi display inside a supermarket in this Southern California town.

There is a long American tradition of immigrant communities dominating certain business sectors, recruiting their compatriots and building their way to the middle class. Many examples are familiar. Greek diners. Chinese laundries. Vietnamese nail salons.