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We study chaotic behavior and diffusion in the 2D periodic Lorentz gas in thefinite-horizon regime. The dynamical observable which we consider is the lengthof single particle's trajectories, which moves in a triangular array of rigiddisks. To analyze the chaoticity of this system, we construct a matrix of thelength of trajectories and perform a level spacing analysis of the spectrum ofthis matrix. We find that a universal behavior occurs both in level spacingdistribution and spectral rigidity. In order to examine diffusion in thisclassical system, we investigate the variance of the length of trajectoriesversus number of collisions to disks. In the case where there is afinite-horizon, such a variance scales linearly with number of bounces. Thisshows that a normal diffusion exists and a central limit theorem is maintainedin this regime.

Fluctuation Statistics and Diffusive Properties of the 2D Triangular Lorentz Gas in the Finite-Horizon Regime