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<p>The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [<CitationRef CitationID="CR8">8</CitationRef>, <CitationRef CitationID="CR40">40</CitationRef>], to any <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\beta &gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and for the eigenvalue counting field.</p>

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Subcritical multiplicative chaos and the characteristic polynomial of the C\(\beta \)E

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月28日

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  • Gaultier Lambert,
  • Joseph Najnudel

摘要

The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular \(\beta \) β -ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular \(\beta \) β -ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [8, 40], to any \(\beta >0\) β > 0 and for the eigenvalue counting field.