  Wave propagation problems for heterogeneous media are known to have many
applications in physics and engineering. Recently, there has been an increasing
interest in stochastic effects due to the uncertainty, which may arise from
impurities of the media. This work considers a two-dimensional wave equation
with random coefficients which may be discontinuous in space. Generalized
polynomial chaos method is used in conjunction with stochastic Galerkin
approximation, and local discontinuous Galerkin method is used for spatial
discretization. Our method is shown to be energy preserving in semi-discrete
form as well as in fully discrete form, when leap-frog time discretization is
used. Its convergence rate is proved to be optimal and the error grows linearly
in time. The theoretical properties of the proposed scheme are validated by
numerical tests.
