  Heavy-tailed distributions naturally occur in many real life problems.
Unfortunately, it is typically not possible to compute inference in closed-form
in graphical models which involve such heavy-tailed distributions.
  In this work, we propose a novel simple linear graphical model for
independent latent random variables, called linear characteristic model (LCM),
defined in the characteristic function domain. Using stable distributions, a
heavy-tailed family of distributions which is a generalization of Cauchy,
L\'evy and Gaussian distributions, we show for the first time, how to compute
both exact and approximate inference in such a linear multivariate graphical
model. LCMs are not limited to stable distributions, in fact LCMs are always
defined for any random variables (discrete, continuous or a mixture of both).
  We provide a realistic problem from the field of computer networks to
demonstrate the applicability of our construction. Other potential application
is iterative decoding of linear channels with non-Gaussian noise.
