  Wireless sensor networks are often used for environmental monitoring
applications. In this context sampling and reconstruction of a physical field
is one of the most important problems to solve. We focus on a bandlimited field
and find under which conditions on the network topology the reconstruction of
the field is successful, with a given probability. We review irregular sampling
theory, and analyze the problem using random matrix theory. We show that even a
very irregular spatial distribution of sensors may lead to a successful signal
reconstruction, provided that the number of collected samples is large enough
with respect to the field bandwidth. Furthermore, we give the basis to
analytically determine the probability of successful field reconstruction.
