This paper describes the story of F. Spitzer’s pioneering work on interacting particle systems. According to the chronological order, the paper is divided into six parts: from the beginning two papers (1969) on deterministic systems with random initial states to the Spitzer’s last models, smoothing and potlach processes and coupled random walk (1981). As a student of Spitzer and as an active member in the group, the author describes vividly the main picture of the development of the subject in the states. This paper is strongly recommended to the readers who are interested in but still unfamiliar with the subject.
Personally, I am also grateful to Frank Spitzer. During March 26, 1984– May 1, 1984, he visited my university. He presented 17 lectures on 8 topics and the last one coincides with his last publication (1986). About 40 people from different parts of the country attended his talks. We learnt a lot not only from his lectures but also from his private advice.