  A rigorous theory for the generation of a large-scale magnetic field by
random non-helically forced motions of a conducting fluid combined with a
linear shear is presented in the analytically tractable limit of low Rm and
weak shear. The dynamo is kinematic and due to fluctuations in the net
(volume-averaged) electromotive force. This is a minimal proof-of-concept
quasilinear calculation aiming to put the shear dynamo, a new effect recently
found in numerical experiments, on a firm theoretical footing. Numerically
observed scalings of the wavenumber and growth rate of the fastest growing
mode, previously not understood, are derived analytically. The simplicity of
the model suggests that shear dynamo action may be a generic property of
sheared magnetohydrodynamic turbulence.
