  The bead model is a random point field on $\mathbb{Z}\times\mathbb{R}$ which
can be viewed as a scaling limit of dimer model. We prove that, in the scaling
limit, the normalized height function of a uniformly chosen random bead
configuration lies in an arbitrarily small neighborhood of a surface $h_0$ that
maximizes some functional which we call as entropy. We also prove that the
limit shape $h_0$ is a scaling limit of the limit shapes of a properly chosen
sequence of dimer models. There is a map from bead configurations to standard
tableaux of a (skew) Young diagram, and the map preserves uniform measures, and
our results of the bead model yield the existence of the limit shape of a
random standard Young tableau.
