6 papers
A submartingale for the probability of avoiding the origin in one-point interaction ground-state diffusion:
Barkat Mian
We study the near-origin behavior on of the singular diffusion whose transition density is given by a Doob transform of the integral kernel of the semigroup generated by th…
Pathwise structure of the three-dimensional attractive one-point interaction diffusion
Barkat Mian
We study the pathwise behavior of the three-dimensional attractive one-point interaction diffusion whose law was constructed by Cranston, Koralov, Molchanov and Vainberg, correspon…
A dyadic construction of a three-dimensional attractive point interaction Markov family
Barkat Mian
We discuss a probabilistic approximation framework for the three-dimensional attractive point interaction on a finite time horizon. By iterating the Doob transforms of the explicit…
Planar diffusions with a point interaction on a finite time horizon
Barkat Mian
The skew-product diffusion [Ann. Appl. Probab. 35, 3150--3214 (2025)] and exponentially tilted planar Brownian motion [Electron. J. Probab. 30, 1--97 (2025)] are canonical examples…
Continuum polymer measures corresponding to the critical 2d stochastic heat flow
Jeremy Clark, Barkat Mian
We construct continuum directed polymer measures corresponding to the critical 2d stochastic heat flow (2d SHF) introduced by Caravenna, Sun, and Zygouras in their recent article […
On planar Brownian motion singularly tilted through a point potential
Jeremy Clark, Barkat Mian
We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval , having transition density functions that are expressible in terms…