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We present a new framework for calculating multi-jet
observables through a resummation of hard emission. The
framework is based on the high energy factorisation of
amplitudes, with the region of applicability extended by
constraining the analytic properties of the scattering
amplitudes according to other known all-order results. As
an example of application we study predictions for Higgs
Boson production through gluon fusion at the LHC in
association with at least two jets. The result is matched
to the tree level matrix elements for 2 and 3 jet
production, and implemented in a Monte Carlo generator.