Baton Rouge, La. — For three hours last Saturday morning, the ''big man'' on Louisiana State University's campus was a 1,200-pound Bengal tiger named Mike. Pranksters broke into the LSU mascot's cage and let it roam free about 1 a.m. , police said. Fortunately, the campus was nearly deserted because of the long Thanksgiving holidays, and Mike's prowl proved uneventful. The tiger was eventually tranquilized and, at last report, resting peacefully in his cage.