rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Limit Shape Problem for Ensembles of Young Diagrams
  name:
    name part: Hora, Akihito.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ja
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: IX, 73 p. 9 illus. online resource.
  abstract: 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. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital studies on harmonic analysis of huge symmetry structures. As mathematics, an asymptotic theory of representations is developed of the symmetric groups of degree n as n goes to infinity. The framework of rigorous limit theorems (especially the law of large numbers) in probability theory is employed as well as combinatorial analysis of group characters of symmetric groups and applications of Voiculescu's free probability. The central destination here is a clear description of the asymptotic behavior of rescaled profiles of Young diagrams in the Plancherel ensemble from both static and dynamic points of view.
  table of contents: 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.
  note: by Akihito Hora.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: System theory
  subject:
    topic: Probabilities
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Complex Systems
  subject:
    topic: Statistical Physics and Dynamical Systems
  classification: QA401-425
  classification: QC19.2-20.85
  classification: 530.15
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematical Physics, 17
  identifier: 9784431564874
  identifier: http://dx.doi.org/10.1007/978-4-431-56487-4
  record info:
    record creation date: 161110
    record change date: 20161110081432.0
    record identifier: 978-4-431-56487-4