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<p>In this paper we prove a scaling limit result for the component of the root in the Wired Minimal Spanning Forest (WMSF) of the Poisson-Weighted Infinite Tree (PWIT), where the latter tree arises as the local weak limit of the Minimal Spanning Tree (MST) on the complete graph endowed with i.i.d. weights on its edges. The limiting object <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {M}^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">M</mi> </mrow> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> can be obtained by aggregating independent Brownian trees using two types of gluing procedures: one that we call the <i>Brownian tree aggregation process</i> and resembles the so-called <i>stick-breaking construction of the Brownian tree</i>; and another one that we call the <i>chain</i> construction, which simply corresponds to gluing a sequence of metric spaces along a line.</p>

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The scaling limit of the root component in the Wired Minimal Spanning Forest of the Poisson Weighted Infinite Tree

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Omer Angel,
  • Delphin Sénizergues

摘要

In this paper we prove a scaling limit result for the component of the root in the Wired Minimal Spanning Forest (WMSF) of the Poisson-Weighted Infinite Tree (PWIT), where the latter tree arises as the local weak limit of the Minimal Spanning Tree (MST) on the complete graph endowed with i.i.d. weights on its edges. The limiting object \(\mathcal {M}^\infty \) M ∞ can be obtained by aggregating independent Brownian trees using two types of gluing procedures: one that we call the Brownian tree aggregation process and resembles the so-called stick-breaking construction of the Brownian tree; and another one that we call the chain construction, which simply corresponds to gluing a sequence of metric spaces along a line.