Random Walk with a Boundary Line as a Free Massive Boson with a Defect Line

TL;DR

This paper maps the problem of a boundary-attractive random walk onto a free massive bosonic quantum field theory with a defect line, enabling the use of boundary S-matrix and form factor techniques to analyze its properties.

Contribution

It introduces a novel mapping between boundary random walks and quantum field theory with defects, facilitating new analytical methods.

Findings

Mapped boundary random walk to quantum field theory with a defect

Applied boundary S-matrix and form factor techniques to analyze the walk

Provided new insights into the statistical properties of boundary-attractive random walks

Abstract

We show that the problem of Random Walk with boundary attractive potential may be mapped onto the free massive bosonic Quantum Field Theory with a line of defect. This mapping permits to recover the statistical properties of the Random Walks by using boundary $S$--matrix and Form Factor techniques.