Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue.

The Limit Shape Problem for Ensembles of Young Diagrams

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 17)

DOI: 10.1007/978-4-431-56487-4

ISBN: 978-4-431-56485-0

Publisher: Springer Japan - Springer Journals

Nov 11, 2016

LitStream

Chapter 1Preliminaries

Hora, Akihito

Pages: 1 –13

[In this chapter, we briefly sketch the following materials as preliminaries for later chapters: representations of the symmetric group and Young diagrams, the Young graph and the Thoma simplex, combinatorial aspects of free probability theory.]
LitStream

Chapter 2Analysis of the Kerov–Olshanski Algebra

Hora, Akihito

Pages: 15 –30

[In this chapter, we investigate the algebra of polynomial functions in coordinates of Young diagrams as a nice framework in which various quantities on Young diagrams can be efficiently computed. This algebra was introduced by Kerov–Olshanski [20], analysis of which is substantially due to...
LitStream

Chapter 3Continuous Diagram

Hora, Akihito

Pages: 31 –41

[In this chapter, continuous diagrams are introduced as limiting objects of the profiles of Young diagrams. It is important that the notion of a transition measure is extended for a continuous diagram.]
LitStream

Chapter 4Static Model

Hora, Akihito

Pages: 43 –60

[Since the Plancherel measure on the path space of the Young graph is ergodic, some deterministic aspects will appear in a macroscopic point of view. In this chapter, we describe the famous limit shape problem for the profiles of random Young diagrams in the Plancherel ensemble, which is due to...
LitStream

Chapter 5Dynamic Model

Hora, Akihito

Pages: 61 –68

[In this chapter, we discuss a dynamical aspect of the limit shape problem for random Young diagrams. In a microscopic point of view, a continuous time Markov chain is introduced on the Young diagrams of size n which keeps the Plancherel measure invariant and has an initial distribution admitting...

results per page

Prev
1
Next

Browse All eBooks