  Classical multiuser information theory studies the fundamental limits of
models with a fixed (often small) number of users as the coding blocklength
goes to infinity. This work proposes a new paradigm, referred to as {\em
many-user information theory}, where the number of users is allowed to grow
with the blocklength. This paradigm is motivated by emerging systems with a
massive number of users in an area, such as machine-to-machine communication
systems and sensor networks. The focus of the current paper is the {\em
many-access} channel model, which consists of a single receiver and many
transmitters, whose number increases unboundedly with the blocklength.
Moreover, an unknown subset of transmitters may transmit in a given block and
need to be identified. A new notion of capacity is introduced and characterized
for the Gaussian many-access channel with random user activities. The capacity
can be achieved by first detecting the set of active users and then decoding
their messages.
