Nicole Richie and Joel Madden linked arms yesterday as they shopped around LA following a lunch date. There was more excitement in store than just getting new goods at Supreme. He tweeted about meeting the rapper Dizzee Rascal, writing, "met one of my favorite artists today Dizzee Rascal — dude was as real and humble as it gets." The happy couple are hanging out at home in LA following Joel's whirlwind world tour over the Summer. Sharing his Good Charlotte diary from the road, Joel revealed sweet photos of Harlow and Sparrow Madden during their family times between gigs. Nicole, meanwhile, has been fully focused on her fashion endeavors. She hosted an event at the Beverly Center last week for Fashion's Night Out and has been busy taping The Fashion Star with Jessica Simpson.