  Consider the lattice of all Young diagrams ordered by inclusion, and denote
by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials,
we endow the edges of the graph Y with formal multiplicities depending on a
real parameter $\theta$. The multiplicities determine a potential theory on the
graph Y. Our main result identifies the corresponding Martin boundary with an
infinite-dimensional simplex, the ``geometric boundary'' of the Young graph Y,
and provides a canonical integral representation for non-negative harmonic
functions.
  For three particular values of the parameter, the theorem specializes to
known results: the Thoma theorem describing characters of the infinite
symmetric group, the Kingman's classification of partition structures, and the
description of spherical functions of the infinite hyperoctahedral Gelfand
pair.
