Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-25 DOI:10.1007/s11040-023-09472-7

Dan Betea, Jérémie Bouttier, Harriet Walsh

引用次数: 0

Abstract

We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universality classes as one-dimensional momentum-space models of free fermions in flat confining potentials, studied by Le Doussal, Majumdar and Schehr. These universality classes involve critical exponents of the form \(1/(2m+1)\), with m a positive integer, and asymptotic distributions given by Fredholm determinants constructed from higher order Airy kernels, extending the generic Tracy–Widom GUE distribution recovered for \(m=1\). We also compute limit shapes for the multicritical Schur measures, discuss the finite temperature setting, and exhibit an exact mapping to the multicritical unitary matrix models previously encountered by Periwal and Shevitz.

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多临界舒尔量和特雷西-维多姆分布的高阶类似物

摘要我们介绍了多临界舒尔量，它们是整数分区上的概率规律，在其边缘产生非一般波动。它们与 Le Doussal、Majumdar 和 Schehr 研究的平面约束势中自由费米子的一维动量空间模型属于相同的普遍性类别。这些普遍性类别涉及临界指数的形式为\(1/(2m+1)\)的临界指数，m 为正整数，以及由高阶艾里核构建的弗雷德霍姆行列式给出的渐近分布，扩展了为\(m=1\)恢复的通用特雷西-维多姆 GUE 分布。我们还计算了多临界舒尔量的极限形状，讨论了有限温度设置，并展示了与佩里瓦尔和谢维茨之前遇到的多临界单元矩阵模型的精确映射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.