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In this paper we prove two asymptotic estimates for pairs of closedtrajectories for open billiards similar to those established by Pollicott andSharp for closed geodesics on negatively curved compact surfaces. The first ofthese estimates holds for general open billiards in any dimension. The moreintricate second estimate is established for open billiards satisfying the socalled Dolgopyat type estimates. This class of billiards includes all openbilliards in the plane and open billiards in $\R^N, N \geq 3$ satisfying someadditional conditions.

Correlations for pairs of periodic trajectories for open billiards