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

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.

17 pages, Latex, 3 figures included

References in corpus (5)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Factorized Scattering in the Presence of Reflecting Boundaries
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• Universal Properties of Self-Avoiding Walks from Two-Dimensional Field Theory
• Exact Theory of Polymer Adsorption in Analogy with the Kondo Problem