A Unitary Matrix Model for $q$-deformed Plancherel Growth
Suvankar Dutta,
Debangshu Mukherjee,
Sanhita Parihar
Abstract:In this paper we construct a unitary matrix model that captures the asymptotic growth of Young diagrams under q-deformed Plancherel measure. The matrix model is a q analog of Gross-Witten-Wadia (GWW) matrix model. In the large N limit the model exhibits a third order phase transition between no-gap and gapped phases, which is a q-deformed version of the GWW phase transition. We show that the no-gap phase of this matrix model captures the asymptotic growth of Young diagrams equipped with q-deformed Plancherel m… Show more
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