Scaling limits for random processes from the point of view of group cohomology (Women in Mathematics)

Abstract

Scaling limits for random walks and stochastic interacting systems have been intensively studied for decades and still remain one of the very major themes of probability theory. I have mainly worked on the diffusive scaling limits in space-time for interacting particle systems, in which I have recently revealed the importance of a group cohomological view and its connection with the Hodge decomposition as well as periodic matrices with collaborators. This structure is expected to be common and effective not only for interacting particle systems but also in the case of one-particle random walks and in homogenization problems. I would like to introduce this connection between the scale limits for random processes and the group cohomology.