Back when he was a boy, Manuel Weintraub’s world revolved around Water Street, the spine of Jewish life here, where newcomers from Russia, Latvia, Austria, and Lithuania would go to shop, chat, and hear the latest gossip. They might stop at one of three bakeries or three kosher butchers, or drop by for a pastrami sandwich at the deli started by his parents, Sam and Ida.

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“It was a place you would go to be with your own,” recalls Mr. Weintraub, who started working at the deli as soon as he could clear a table and for most of the next 50 years spent 12- to 15-hour days making sandwiches, slicing corned beef, and schmoozing. The world of Jewish immigrants moved past his windows and poured into the 14 vinyl booths.

It’s different now, though, as it is for many of Weintraub’s generation. About 20 percent of the country’s 20 million adult second-generation immigrants, the term for American children with at least one foreign-born parent, are 65 or older, according to the Pew Research Center’s analysis of US Census data. Most are descendants of people like Sam and Ida Weintraub, who came to this country in what is called the “second wave” of immigration to the United States.

Although these second-generation immigrants might maintain an ethnic identity – Italian, German, Jewish – they are, by many measures, fully assimilated, dispersing into previously Anglo communities and filling all varieties of professional jobs; their children are even more likely to marry outside their ethnic group and speak English rather than the tongue of the old country.

These children of immigrants may have changed US society with them – think spaghetti and meatballs or pastrami on rye – but for themselves, there’s no question: They’re American.

“We have this phenomenon in the United States where we have hyphenated identities. You can retain a cultural identity and still be an assimilated person,” says Jacob Vigdor, public policy expert at Duke University in Durham, N.C., who created an “assimilation index” to gauge immigrant integration. “Your ethnicity and national identity are not wrapped up together. If you were to describe yourself as a Chinese-American, nobody would bat an eye. You can think of yourself as American, as in that’s the country to which you belong, and also think of yourself as a member of an ethnic group.”

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