Scholarlink

<p>In the elementary and self-contained study we prove that in any natural spatial dimension <i>d</i> the small deviations of a Gaussian multiplicative chaos (GMC) <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10197_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mi>γ</mi> </msub> </math></EquationSource> </InlineEquation> are of lognormal type. We place the small deviations in the context of the regime of positive definiteness for a strictly logarithmic covariance kernel and provide the explicit bounds on the associated constants. We also provide a new representation of the Laplace transform of GMC related to a strictly logarithmic covariance kernel.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Small Deviations of Gaussian Multiplicative Chaos with A Strictly Logarithmic Covariance on Euclidean Ball

  • 期刊论文

  • 发表日期：

    2025年2月20日

查看全文
  • Anna Talarczyk,
  • Maciej Wiśniewolski

摘要

In the elementary and self-contained study we prove that in any natural spatial dimension d the small deviations of a Gaussian multiplicative chaos (GMC) \(M_\gamma \) M γ are of lognormal type. We place the small deviations in the context of the regime of positive definiteness for a strictly logarithmic covariance kernel and provide the explicit bounds on the associated constants. We also provide a new representation of the Laplace transform of GMC related to a strictly logarithmic covariance kernel.