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Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the asymptotic decay of the survival probability is exponential and characterized by an escape rate, which can be related to the average positive Lyapunov exponent and to the dimension of the fractal repeller of the system. For infinite systems, the survival probabilitydoi:10.1016/j.physd.2003.09.009 fatcat:z7drnyiqlbcxxfnh46t6cxl7gq