The limit shape problem for ensembles of young diagrams / Akihito Hora.

Preface; Contents; 1 Preliminaries; 1.1 Representations of Symmetric Groups; 1.2 Young Graph; 1.3 Free Probability; 2 Analysis of the Kerov
Olshanski Algebra; 2.1 Coordinates of a Young Diagram; 2.2 Transition Measure I; 2.3 The Kerov
Olshanski Algebra; 3 Continuous Diagram; 3.1 Continuous Diagram I; 3.2 Transition Measure II; 3.3 Continuous Diagram II; 4 Static Model; 4.1 Balanced Young Diagrams; 4.2 Convergence to the Limit Shape; 4.3 Continuous Hook and the Limit Shape; 4.4 Approximate Factorization Property; 5 Dynamic Model; 5.1 Restriction-Induction Chain; 5.2 Diffusive Limit