Stochastic many-body delta-Bose gas in two dimensions

Schrodinger operators with delta-function potentials have a long history in the literature and also receive renewed interest in other areas, such as the Kardar–Parisi–Zhang equation. Such operators have the characteristics for allowing closed analytic solutions, but the solution forms and methods differ drastically by spatial dimensions. This talk will introduce a Feynman–Kac-type formula representing the semigroup of the many-body delta-Bose gas in two dimensions. The associated stochastic description primarily concerns constructing singular diffusions that allow the interpretation of multiple two-dimensional Brownin motions conditioned to contact. The main discussion in this talk will consider these diffusions accordingly.