大葉大學圖書館 |

The limit shape problem for ensembles of young diagrams[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.3
書名/作者:	The limit shape problem for ensembles of young diagrams/ by Akihito Hora.
作者:	Hora, Akihito.
出版者:	Tokyo : : Springer Japan :, 2016.
面頁冊數:	ix, 73 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Limit cycles.
標題:	Mathematics.
標題:	Mathematical Physics.
標題:	Topological Groups, Lie Groups.
標題:	Group Theory and Generalizations.
標題:	Probability Theory and Stochastic Processes.
標題:	Complex Systems.
標題:	Statistical Physics and Dynamical Systems.
ISBN:	9784431564874
ISBN:	9784431564850
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-4-431-56487-4

The limit shape problem for ensembles of young diagrams[electronic resource] /
Hora, Akihito.

The limit shape problem for ensembles of young diagrams[electronic resource] /by Akihito Hora. - Tokyo :Springer Japan :2016. - ix, 73 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.172197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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.

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.

ISBN: 9784431564874

Standard No.: 10.1007/978-4-431-56487-4doiSubjects--Topical Terms:

470162
Limit cycles.

LC Class. No.: QA371

Dewey Class. No.: 515.3

The limit shape problem for ensembles of young diagrams[electronic resource] /
LDR:02435nam a2200325 a 4500 001 476711
003 DE-He213
005 20161110081432.0
006 m d
007 cr nn 008maaau
008 181208s2016 ja s 0 eng d
020 $a 9784431564874 $q (electronic bk.)
020 $a 9784431564850 $q (paper)
024 7 $a 10.1007/978-4-431-56487-4 $2 doi
035 $a 978-4-431-56487-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
082 0 4 $a 515.3 $2 23
090 $a QA371 $b .H811 2016
100 1 $a Hora, Akihito. $3 687690
245 1 4 $a The limit shape problem for ensembles of young diagrams $h [electronic resource] / $c by Akihito Hora.
260 $a Tokyo : $b Springer Japan : $b Imprint: Springer, $c 2016.
300 $a ix, 73 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.17
505 0 $a 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.
520 $a 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.
650 0 $a Limit cycles. $3 470162
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Mathematical Physics. $3 465111
650 2 4 $a Topological Groups, Lie Groups. $3 464896
650 2 4 $a Group Theory and Generalizations. $3 464956
650 2 4 $a Probability Theory and Stochastic Processes. $3 463894
650 2 4 $a Complex Systems. $3 465366
650 2 4 $a Statistical Physics and Dynamical Systems. $3 671437
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematical physics ; $v v.1. $3 591158
856 4 0 $u http://dx.doi.org/10.1007/978-4-431-56487-4
950 $a Mathematics and Statistics (Springer-11649)