On planar Brownian motion singularly tilted through a point potential

2023/06/26 by Clark, Jeremy, Mian, Barkat · 2 citations
#60G17 #60J55 #82B44 #82C23 #82D60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.14849

Abstract

We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval [0,T], having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the two-dimensional Schrödinger operator with a point potential at the origin. These diffusions have a singular drift pointing in the direction of the origin that is strong enough to enable the possibly of visiting there, in contrast to a two-dimensional Brownian motion. Our main focus is on characterizing a local time process at the origin analogous to that for a one-dimensional Brownian motion and on studying the law of its process inverse.

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• Conditional GMC within the stochastic heat flow
• On point interactions in two dimensions via additive functionals

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