DIFFUSION IN ONE DIMENSIONAL RANDOM MEDIUM AND HYPERBOLIC BROWNIAN MOTION
Alain COMTET, Cecile MONTHUS
TL;DR
This paper explores the relationship between classical diffusion in a one-dimensional random medium and hyperbolic Brownian motion, analyzing distributions through stochastic calculus and functional integration.
Contribution
It provides a detailed analysis of the connection between diffusion in random media and hyperbolic Brownian motion, using advanced mathematical techniques.
Findings
Derived distributions related to exponential functionals of Brownian motion
Established links between diffusion in random media and hyperbolic geometry
Applied stochastic calculus to study functional integrals in this context
Abstract
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this relationship and study various distributions using stochastic calculus and functional integration.
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