  The problem of optimal node density for ad hoc sensor networks deployed for
making inferences about two dimensional correlated random fields is considered.
Using a symmetric first order conditional autoregressive Gauss-Markov random
field model, large deviations results are used to characterize the asymptotic
per-node information gained from the array. This result then allows an analysis
of the node density that maximizes the information under an energy constraint,
yielding insights into the trade-offs among the information, density and
energy.
