  We consider a Markov evolution of lozenge tilings of a quarter-plane and
study its asymptotics at large times. One of the boundary rays serves as a
reflecting wall.
  We observe frozen and liquid regions, prove convergence of the local
correlations to translation-invariant Gibbs measures in the liquid region, and
obtain new discrete Jacobi and symmetric Pearcey determinantal point processes
near the wall.
  The model can be viewed as the one-parameter family of Plancherel measures
for the infinite-dimensional orthogonal group, and we use this interpretation
to derive the determinantal formula for the correlation functions at any finite
time moment.
