One of Amit P. Mehta’s first cases after becoming a federal judge in late 2014 proved to be a crash course in antitrust.

Sysco, the nation’s largest distributor of food to restaurants and cafeterias, was trying to buy the rival US Foods, and the Federal Trade Commission had sued to block the $3.5 billion deal, arguing that it would stifle competition.

Judge Mehta told lawyers on both sides that he would need help educating himself. Over the next few months, he was a tireless and bright student, according to lawyers for the government and Sysco, absorbing the details of antitrust law and asking sharp questions about precedents, economic theory and the food-distribution business.

After the trial in 2015, Judge Mehta wrote a…