Scholarlink

<p>Consider a rooted <i>N</i>-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible vertices and kill all the others. For any positive constant <i>α</i>, we describe the asymptotic behaviors of the population at the <i>αN</i>-th generation as <i>N</i> goes to infinity. We also study the criticality of the survival probability at the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((eN-\frac{3}{2}{\rm{log}}N)\)</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>e</mi> <mi>N</mi> <mo>−</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mi>N</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>-th generation in this paper.</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

Increasing Paths on N-ary Trees

  • 期刊论文

  • 发表日期：

    2026年6月15日

查看全文
  • Xinxin Chen

摘要

Consider a rooted N-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible vertices and kill all the others. For any positive constant α, we describe the asymptotic behaviors of the population at the αN-th generation as N goes to infinity. We also study the criticality of the survival probability at the \((eN-\frac{3}{2}{\rm{log}}N)\) ( e N − 3 2 l o g N ) -th generation in this paper.