Given a Young diagram ?, we consider a uniform random Young tableau T of shape ?, i.e. a uniform filling of the cells of ? conditioned to have increasing rows and columns. Letting ? go to infinity with some fixed "limiting shape", it is known that the random tableau T converges to some limiting surface. This problem has been investigated through various angles: combinatorics, representation theory, statistical physics, ...
In this talk, we will use a recent determinantal representation of (Poissonized) random tableau, due to Gorin and Rahman, to find a new description of the limit surface for tableaux of multirectangular shape. In particular, we discover that this limiting surface might be discontinuous and characterize exactly when such discontinuities occur.
Joint work with Valentin Feray, Cedric Boutillier and Pierre-Loic Meliot.
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