Scholarlink

Abstract <p> For rescaled additive functionals of the sine process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov–Smirnov metric. Under scaling with coefficient <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1170_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(R&gt;1\)</EquationSource> </InlineEquation>, the Kolmogorov–Smirnov distance is bounded from above by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1170_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(c/\log R\)</EquationSource> </InlineEquation> for a smooth function, and by <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1170_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(c/R\)</EquationSource> </InlineEquation> for a function holomorphic in a horizontal strip. </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

The Speed of Convergence Under the Kolmogorov–Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine Process

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • Alexander Bufetov

摘要

Abstract

For rescaled additive functionals of the sine process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov–Smirnov metric. Under scaling with coefficient \(R>1\) , the Kolmogorov–Smirnov distance is bounded from above by \(c/\log R\) for a smooth function, and by \(c/R\) for a function holomorphic in a horizontal strip.