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We consider uniform random domino tilings of the restricted Aztec diamondwhich is obtained by cutting off an upper triangular part of the Aztec diamondby a horizontal line. The restriction line asymptotically touches the arcticcircle that is the limit shape of the north polar region in the unrestrictedmodel. We prove that the rescaled boundary of the north polar region in therestricted domain converges to the Airy$_2$ process conditioned to stay below aparabola with explicit continuous statistics and the finite dimensionaldistribution kernels. The limit is the hard-edge tacnode process which wasfirst discovered in the framework of non-intersecting Brownian bridges. Theproof relies on a random walk representation of the correlation kernel of thenon-intersecting line ensemble which corresponds to a random tiling.

Fluctuations of the Arctic curve in the tilings of the Aztec diamond on restricted domains