On an imaginary exponential functional of Brownian motion

Details On an imaginary exponential functional of Brownian motion On an imaginary exponential functional of Brownian motion

2011-01-06

arxiv.org/abs/1101.1173v1

J. Phys. A: Math. Theor. 44 (2011) 175003

Physics

Condensed Matter

Statistical Mechanics

30 pages, 9 figures, 3 tables

Scientific paper

10.1088/1751-8113/44/17/175003

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.

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