Barkat Mian

A submartingale for the probability of avoiding the origin in one-point interaction ground-state diffusion: $d \in \{2,3\}$

We study the near-origin behavior on $[0,T]$ of the singular diffusion whose transition density is given by a Doob transform of the integral kernel of the semigroup generated by the $d$-dimensional Schr\"odinger operator $L^{\gamma}$ with a one-point potential at the origin, where the driving family is the ground state...