i.i.d. 矩阵特征多项式的最大值

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2025-04-08 DOI:10.1002/cpa.22250

Giorgio Cipolloni, Benjamin Landon

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引用次数: 0

摘要

我们计算了具有实数项或复数项的i.i.d矩阵的特征多项式最大值的首阶渐近。特别地，这个结果是新的，即使对于真实的Ginibre矩阵，这是一个开放的问题，在Lambert等人。电子。J. Probab. 29 (2024)；复杂的Ginibre案例涵盖在兰伯特，Comm. Math Phys. 378（2020）。这是Fyodorov-Hiary-Keating猜想的一阶项的非厄米式类比的第一个通用性结果。我们的方法是基于通过戴森布朗运动构造与分支随机漫步（BRW）的耦合。特别地，我们发现了实i.i.d矩阵与非齐次BRW之间的新联系。

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Maximum of the characteristic polynomial of i.i.d. matrices

We compute the leading order asymptotic of the maximum of the characteristic polynomial for i.i.d. matrices with real or complex entries. In particular, this result is new even for real Ginibre matrices, which was left as an open problem in Lambert et al. Electron. J. Probab. 29 (2024); the complex Ginibre case was covered in Lambert, Comm. Math Phys. 378 (2020). These are the first universality results for the non‐Hermitian analog of the first order term of the Fyodorov–Hiary–Keating conjecture. Our methods are based on constructing a coupling to the branching random walk (BRW) via Dyson Brownian motion. In particular, we find a new connection between real i.i.d. matrices and inhomogeneous BRW.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.