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The Minimal Position of a Stable Branching Random Walk

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Jingning Liu, Mei Zhang

Probability · Submitted 25 Dec 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We established an integral test to describe the lower limit of $M_n-\frac{1}{\alpha}\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}{\alpha})\log n$.

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arXiv ID1712.08979 (version 1)
Pith IDL3MY3QV7, Pith's permanent record of this paper and its review
CitationJingning Liu, Mei Zhang. "The Minimal Position of a Stable Branching Random Walk." arXiv:1712.08979 (2017). https://pith.science/paper/L3MY3QV7
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,032 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.87 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\alpha-$stable law with $1<\alpha<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\frac{1}{\alpha}\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}{\alpha})\log n$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\alpha-$stable law with $1<\alpha<2$. background 0.67 0.41 0.03 asserted 0.92
s1 Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. background 0.81 0.18 0.03 asserted 0.59
s2 We established an integral test to describe the lower limit of $M_n-\frac{1}{\alpha}\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}{\alpha})\log n$. result 0.89 0.95 0.86 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\alpha-$stable law with $1<\alpha<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\frac{1}{\alpha}\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}{\alpha})\log n$.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 3 sentences without a confident label

Uses the method or tool of 1 paper
  • Now we define for $n<k≤αn$, [equation] where $a_i^(n,λ)=1_{α/4n<i≤k}(1/αlogn-λ)$, $b_i^(k,n)=1_{0≤i≤α/4n}i^γ/2+1_{α/4n<i≤αn}(k-i)^γ/2$, $K>0$, $γ=1/α(α+1)$ and $c'$ is a positive constant chosen as in [ref] .

    On Seneta-Heyde Scaling for a stable branching random walk · Proofs of Theorems 1.1–1.3 · 0.85

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