  Within the effective theory for the Color Glass Condensate, we study
multi-particle production with rapidity correlations in proton-nucleus
collisions at high energy. The high-energy evolution responsible for such
correlations is governed by a generalization of the JIMWLK equation which
describes the simultaneous evolution of the (strong) nuclear color fields in
the direct amplitude and the complex conjugate amplitude. This functional
equation can be used to derive ordinary evolution equations for the
cross-sections for particle production (a generalization of the Balitsky
hierarchy). However, the ensuing equations appear to be too complicated to be
useful in practice, including in the limit where the number of colors is large.
To circumvent this problem, we propose an alternative formulation of the
high-energy evolution as a Langevin process, which is better suited for
numerical implementations. This process is directly oriented towards the
calculation of the cross-sections, so its detailed structure depends upon the
nature of the final state. We present the stochastic equations appropriate for
two gluon production, and also for three gluon production, with generic
rapidity differences.
