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One-point localization for branching random walk in Pareto environment

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Marcel Ortgiese, Matthew I. Roberts

Probability · Submitted 29 Feb 2016

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

The authors' main claim We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential.

how it is stated · asserted 1.00 read the record →

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arXiv ID1602.09049 (version 2)
Pith IDSY4E6GW4, Pith's permanent record of this paper and its review
CitationMarcel Ortgiese, Matthew I. Roberts. "One-point localization for branching random walk in Pareto environment." arXiv:1602.09049 (2016). https://pith.science/paper/SY4E6GW4
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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, 4,190 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.02 · states quantitative result 0.11 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. In our case, we rely on very fine estimates for the behaviour of particles near a good point. This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island.

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 We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. background 0.72 0.28 0.03 asserted 0.91
s1 We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. result 0.99 0.94 0.88 asserted 1.00
s2 The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. background 0.99 0.04 0.05 asserted 1.00
s3 In our case, we rely on very fine estimates for the behaviour of particles near a good point. method 0.99 0.79 0.03 asserted 0.96
s4 This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island. background 0.36 0.86 0.07 asserted 0.98

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

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • 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

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. In our case, we rely on very fine estimates for the behaviour of particles near a good point. This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

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 · 15 sentences without a confident label

Uses the method or tool of 2 papers
  • In fact, in proving Theorem [ref], we will use the results in [ref] to reduce the number of sites that we need to look at; and since we used a rescaled picture in that article, we will again use a rescaling here, to prove a slightly different statement from Theorem [ref] that implies the statement above.

    Intermittency for branching random walk in Pareto environment · Main result · 0.83

  • We use the many-to-two formula [ref] .

    The many-to-few lemma and multiple spines · The population at $y$ is big enough · 1.00

Cites as support 1 paper
Cites as background 1 paper

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