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Abstract: In this paper we show that it is possible to identify the Green's function between two points of a bounded inhomogeneous medium by a cross correlation technique. We consider the situation in which a collection of sources with unknown spatial distribution emit stationary random signals into the medium, which are recorded at the observation points. By using a semi-classical approach we show that the cross correlation of these signals has enough information to identify the singular component of the Green's function. We assume that the underlying classical Hamitonian flow is ergodic and we use the Egorov theorem to control the error between the classical flow and the quantum flow. We also show that this approach is statistically stable when the averaging time is long enough.
Mots Clés: Semiclassical analysis; ergodic theory; inverse problems