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

W. Fang; H.-K. Hwang; M. Kang

doi:10.1016/j.jcta.2020.105363

Phase transitions from exp⁡(n^1/2) to exp⁡(n^2/3) in the asymptotics of banded plane partitions

W. Fang^*, H.-K. Hwang, M. Kang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 ₁n ⁻¹exp⁡(c ₂n ^1/2) to c ₃n ^−49/72exp⁡(c ₄n ^2/3+c ₅n ^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.

Original language	English
Article number	105363
Journal	Journal of Combinatorial Theory, Series B
Volume	178
DOIs	https://doi.org/10.1016/j.jcta.2020.105363
Publication status	Published - 2021

Keywords

Asymptotics
Banded plane partition
Integer partition
Phase transition
Plane partition
Saddle point method

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1016/j.jcta.2020.105363

Cite this

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title = "Phase transitions from exp⁡(n1/2) to exp⁡(n2/3) in the asymptotics of banded plane partitions",

abstract = "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 1n −1exp⁡(c 2n 1/2) to c 3n −49/72exp⁡(c 4n 2/3+c 5n 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. ",

keywords = "Asymptotics, Banded plane partition, Integer partition, Phase transition, Plane partition, Saddle point method",

author = "W. Fang and H.-K. Hwang and M. Kang",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

doi = "10.1016/j.jcta.2020.105363",

language = "English",

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AU - Fang, W.

AU - Hwang, H.-K.

AU - Kang, M.

PY - 2021

Y1 - 2021

N2 - 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 1n −1exp⁡(c 2n 1/2) to c 3n −49/72exp⁡(c 4n 2/3+c 5n 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.

AB - 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 1n −1exp⁡(c 2n 1/2) to c 3n −49/72exp⁡(c 4n 2/3+c 5n 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.

KW - Asymptotics

KW - Banded plane partition

KW - Integer partition

KW - Phase transition

KW - Plane partition

KW - Saddle point method

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