A weighted 'pure snake' model on a torus is shown to be exactly solvable, and its scaling limit yields a new representation of ASEP on a ring as a change of measure from non-colliding walkers.
Limit shapes of large skew Young tableaux and a modification of the TASEP process
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abstract
We present a survey of points of view on the problem of the asymptotic shape of a path between two large Young diagrams, and introduce a modification of the TASEP process related to it. This representation allows to write explicitly the functional, counting the asymptotics of the number of Young tableau close to a given one, as well as to see the sine-process on the boundary shape of a large random Young diagram.
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The Integrable Snake Model
A weighted 'pure snake' model on a torus is shown to be exactly solvable, and its scaling limit yields a new representation of ASEP on a ring as a change of measure from non-colliding walkers.