Double-scaling limits of Toeplitz determinants and Fisher-Hartwig singularities

被引：1

作者：

Virtanen, Jani A. ^{[1
]}

机构：

[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

来源：

DIVERSITY AND BEAUTY OF APPLIED OPERATOR THEORY | 2018年 / 268卷

基金：

英国工程与自然科学研究理事会;

关键词：

Toeplitz determinants; Szego asymptotics; Fisher-Hartwig singularities; double-scaling limits; ASYMPTOTIC-BEHAVIOR; ISING-MODEL; CONJECTURE; MATRICES;

D O I：

10.1007/978-3-319-75996-8_29

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Double-scaling limits of Toeplitz determinants D-n(f(t)) generated by a set of functions f(t) is an element of L-1 are discussed as both n -> infinity and t -> 0 simultaneously, which is currently of great importance in mathematics and in physics. The main focus is on the cases where the number of Fisher-Hartwig singularities changes as t -> 0. All the results on double-scaling limits are discussed in the context of applications in random matrix theory and in mathematical physics.

引用

页码：495 / 504

页数：10

共 39 条

[1] Uniform Asymptotics of Toeplitz Determinants with Fisher-Hartwig Singularities
Fahs, B.
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021, 383 (02) : 685 - 730
[2] Asymptotics of Toeplitz, Hankel, and Toeplitz plus Hankel determinants with Fisher-Hartwig singularities
Deift, Percy
Its, Alexander
Krasovsky, Icor
[J]. ANNALS OF MATHEMATICS, 2011, 174 (02) : 1243 - 1299
[3] Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit
Ivanov, Dmitri A.
Abanov, Alexander G.
Cheianov, Vadim V.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (08)
[4] A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities
Ehrhardt, T
[J]. RECENT ADVANCES IN OPERATOR THEORY: ISRAEL GOHBERG ANNIVERSARY VOLUME, 2000, 124 : 217 - 241
[5] Toeplitz determinants with one Fisher-Hartwig singularity
Ehrhardt, T
Silbermann, B
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (01) : 229 - 256
[6] TOEPLITZ MATRICES AND DETERMINANTS WITH FISHER-HARTWIG SYMBOLS
BOTTCHER, A
SILBERMANN, B
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1985, 63 (02) : 178 - 214
[7] Schatten norms of Toeplitz matrices with Fisher-Hartwig singularities
Boettcher, Albrecht
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2006, 15 : 251 - 259
[8] Unitarily invariant norms of Toeplitz matrices with Fisher-Hartwig singularities
Vong, Seak-Weng
Jin, Xiao-Qing
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2007, 29 (03) : 850 - 854
[9] TOEPLITZ DETERMINANTS WITH SYMBOLS FROM THE FISHER-HARTWIG CLASS
BOTTCHER, A
SILBERMANN, B
[J]. DOKLADY AKADEMII NAUK SSSR, 1984, 278 (01): : 13 - 16
[10] Toeplitz determinants, Fisher-Hartwig symbols, and random matrices
Basor, Estelle L.
[J]. RECENT PERSPECTIVES IN RANDOM MATRIX THEORY AND NUMBER THEORY, 2005, 322 : 309 - 336

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