Phase transitions from exp(n1/2) to exp(n2/3) in the asymptotics of banded plane partitions

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Fang, Wenjie¹  Hwang, Hsien-Kuei²  Kang, Mihyun³ 

[1] Univ Gustave Eiffel, LIGM, ESIEE Paris, CNRS, F-77454 Marne La Vallee, France

[2] Acad Sinica, Inst Stat Sci, Taipei 11529, Taiwan

[3] Graz Univ Technol, Inst Discrete Math, A-8010 Graz, Austria

关键词: Banded plane partition;    Asymptotics;    Phase transition;    Saddle point method;    Integer partition;    Plane partition;   

DOI  :  10.1016/j.jcta.2020.105363

来源: Elsevier

【 摘 要 】

We examine the asymptotics of a class of banded plane partitions under a varying bandwidth parameter m, and clarify the transitional behavior for large size n and increasing m = m(n) to be from c(1)n(-1) exp(c(2)n(1/2)) to c(3)n(-49/72) exp (c(4)n(2/3) + c(5)n(1/3)) for some explicit coefficients c(1), ..., c(5). The method of proof, which is a unified saddle-point analysis for all phases, is general and can be extended to other classes of plane partitions. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free