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Synchronization of two replicas of coupled map lattices for continuous mapsis known to be in the multiplicative noise universality class. We study thistransition in the presence of quenched disorder in coupling. The disorder isidentical in both replicas. We study one-dimensional, two-dimensional, andglobally coupled logistic and tent maps. We observe a clear second-ordertransition with new exponents. The order parameter decays as $t^{-\delta}$ and$\delta$ depends on the map and its parameters. The asymptotic order parameterfor $\Delta$ distance from a critical point grows as $\Delta^{\beta}$ with$\beta=\delta$. The quenched disorder in coupling is a relevant perturbationfor the replica synchronization of coupled map lattices. The critical exponentsare different from those of the multiplicative noise universality class.However, it does not depend on dimensionality if the transition is continuousfor the cases studied.

Synchronization transition in space-time chaos in the presence of quenched disorder