On an imaginary exponential functional of Brownian motion

Abstract

We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary annihilation process, within the Doi-Peliti formalism for reaction-diffusion systems. The main emphasis is put on the complementarity between the usual Langevin approach and another approach based on the similarity with Kesten variables and other one-dimensional disordered systems. Even though neither of these routes leads to the full solution of the problem, we have obtained a collection of results describing various regimes of interest.

30 pages, 9 figures, 3 tables

References in corpus (2)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Imaginary noise and parity conservation in the reaction A+A <--> 0

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