James Ritchie Norris (born 29 August 1960) is a mathematician working in probability theory and stochastic analysis. He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge. He has made contributions to areas of mathematics connected to probability theory and mathematical analysis, including Malliavin calculus, heat kernel estimates, and mathematical models for coagulation and fragmentation. He was awarded the Rollo Davidson Prize in 1997.