Gunners are back at the top of the table after victory at Wolves on Saturday.
"Yes, I do," Walcott said when asked if Arsenal will win the league.
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"It's these games I don't think you're going to have to get yourself up for, you're just made for it. These are players that want to make the difference and to create history and to change that pattern.
"City, I feel like Brighton and Tottenham, they've got a lot to say. Liverpool again, Fulham away, Everton away. There's some tough fixtures. But Arsenal, I expect them to get the points in those games."