The Limit Shape Problem for Ensembles of Young Diagrams

ISBN-13: 9784431564850 / Angielski / Miękka / 2016 / 73 str.

Akihito Hora

Opis

This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit.

Spis treści

1. Introduction.- 2. Prerequisite materials.- 2.1 representations of the symmetric group.- 2.2 free probability.- 2.3 ensembles of Young diagrams.- 3. Analysis of the Kerov—Olshanski algebra.- 3.1 polynomial functions of Young diagrams.- 3.2 Kerov polynomials.- 4. Static model.- 4.1 Plancherel ensemble.- 4.2 Thoma and other ensembles.- 5. Dynamic model.- 5.1 hydrodynamic limit for the Plancherel ensemble.