How does Arthur Miller demonstrate the difficulties which immigrants face?

A View from the Bridge is largely concerned with the American immigrant experience. Arthur Miller, however, isn't simply making a point about immigration; he's also proffering wider reflections on the United States as a nation of immigrants.
The very title of the play underlines the difficulties that immigrants face in New York. The Brooklyn Bridge is a symbol of the large gap that separates newcomers from established citizens. Rodolpho and Marco seem destined never to bridge that gap. For one thing, they immigrated illegally, and they could be rounded up and deported at any moment. They're also homesick, although Rodolpho, unlike Marco, ultimately plans to stay in the United States.
That sense of insecurity they feel as immigrants seeps its way into Eddie's home when the two men come to stay with him. Before long, Eddie too becomes a stranger, only this time in his own home. Unlike the two Italians, he belongs in New York; this is truly his spiritual home. Yet as Rodolpho and Marco begin to take over his domestic life, he starts to get some idea of what it means not to have a secure place in the world.
But this realization does not, as it should, bring Eddie wisdom. He's much too jealous of Rodolpho's courtship of Catherine to feel any genuine empathy for him or Marco. His blood-ties to the men count for nothing; any ethnic solidarity he may have felt has been clouded by his uncontrollable lust for Catherine.
When Eddie calls the Immigration Office, he becomes alienated from his own ethnicity, his own immigrant heritage. He still retains a limited perspective on things, his very own "view from the bridge." Although he's an Italian American as opposed to an Italian, he still thinks as his ancestors did all those years ago. Ironically, it is Rodolpho the immigrant who is the more American of the two with his desire to settle down and take a shot at the American dream.
Marco's fatal attack upon Eddie towards the end of the play is highly symbolic. In the conflict between the old world and the new, Miller suggests that one never can, nor should, attempt to hide or repress one's immigrant heritage, no matter how hard one tries. It is an integral part of one's identity. Aside from the obvious considerations of homesickness and finding a job and a place to stay, the greatest difficulty for immigrants lies is reconciling their Americanism with their heritage. And this is one conflict that Eddie Carbone never quite manages to resolve.