In this paper we study the existing observation in literature about synchronization of a large number of coupled maps with random nonlocal connectivity @Chate and Manneville, Chaos 2, 307 ~1992!#. These connectivities which lack any spatial significance can be realized in neural nets and electrical circuits. It is quite interesting and of practical importance to note that a huge number of maps can be synchronized with this connectivity. We show that this synchronization stems from the fact that the connectivity matrix has a finite gap in the eigenvalue spectrum in the macroscopic limit. We give a quantitative explanation for the gap. We compare the analytic results with the ones quoted in the above reference. We also study the departures from this highly collective behavior in the low connectivity limit and show that the behavior is almost statistical for very low connectivity. Of late, there has been considerable attention paid to the study of coupled map lattices ~CML! in various contexts. They have been used as a computationally simple and analytically tractable model for spatiotemporal systems @1#. The studies on CML’s have been either in one and two dimensional lattices or with global coupling, in which case there is no notion of lattice geometry @2#. The higher dimensional connectivities @3# or hierarchial connectivities @4,5# are studied very little. One more system that has been studied is the CML with random nonlocal couplings @6#. The motivation is twofold. First, this is an effectively high dimensional system. The phenomenology in CML in higher dimensions has not been studied much, and needs further investigation. Second, there are systems like neural nets in which the local connections do not have any spatial significance. There also exist systems like electrical circuits @7# in which connectivity is at one’s will and such a coupling can be easily realized. Thus the studies of different connectivities and their effects will be useful in designing well controlled systems. In this system of random nonlocal connectivity Chate and Manneville have presented preliminary results @6# which show that synchronization of a large number of oscillators is easily achieved with this connectivity. Synchronization of oscillators in spatially extended systems such as coupled oscillators is important from various points of view. By achieving synchronization, one can try to build huge but more controllable and better behaved systems which are effectively low dimensional @7#. Sometimes, synchronization may serve other purposes, such as sending codes that are difficult to break @8#. In various contexts, this problem has been subjected to several studies in the past few years @9#. We would like to show that the phenomenon of synchronization can be generally understood by investigating the eigenvalue spectrum of the connectivity matrix and can help us to understand the existing observations. In this paper, we will explicitly illustrate how one can separate the mode leading to spatial homogeneity from the rest. We will show that there exists a finite gap between the growth rates, the spatially homogeneous mode, and the rest in the model studied in Ref. @6#. We will also study the departures from this behavior for lower connectivities. For the linear stability analysis of the synchronized state, we will study the eigenvalue spectrum of the connectivity matrix with random nonlocal connectivity. We will also study the eigenspectrum of the product of such matrices. We would note that a similar model of random connectivity matrix of size N3N with k nonzero elements in each row has been investigated by Cook and Derrida in Ref. @10# in connection with the random energy model, the generalized random energy model, and directed polymers in random media. They have obtained exact analytic results for products of such matrices in the case where the matrices are sparse and the distribution function of nonzero elements is not a d function. However, in the model studied by Chate and Manneville @6#, all connections have the same weight, i.e., the distribution function of nonzero elements is a d function.