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Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process

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Olof Elias, Johan Tykesson

Probability · Submitted 26 Sep 2017

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

The authors' main claim Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.

how it is stated · asserted 1.00 read the record →

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arXiv ID1709.09052 (version 1)
Pith IDAUAK2H7W, Pith's permanent record of this paper and its review
CitationJohan Tykesson, Olof Elias. "Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process." arXiv:1709.09052 (2017). https://pith.science/paper/AUAK2H7W
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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, 4,178 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.31 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider the Brownian interlacements model in Euclidean space, introduced by A.S. Sznitman in \cite{sznitman2013scaling}. We give estimates for the asymptotics of the visibility in the vacant set. We also consider visibility inside the vacant set of the Brownian excursion process in the unit disc and show that it undergoes a phase transition regarding visibility to infinity as in \cite{benjamini2009visibility}. Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.

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 the Brownian interlacements model in Euclidean space, introduced by A.S. background 0.90 0.22 0.03 unclear 0.59
s1 Sznitman in \cite{sznitman2013scaling}. background 1.00 0.03 0.02 unclear 0.79
s2 We give estimates for the asymptotics of the visibility in the vacant set. contribution 0.52 0.94 0.38 asserted 0.99
s3 We also consider visibility inside the vacant set of the Brownian excursion process in the unit disc and show that it undergoes a phase transition regarding visibility to infinity as in \cite{benjamini2009visibility}. result 0.52 0.87 0.27 asserted 1.00
s4 Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity. result 0.99 0.94 0.36 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
  • full text
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  • references and citing sentences
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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

We consider the Brownian interlacements model in Euclidean space, introduced by A.S. Sznitman in \cite{sznitman2013scaling}. We give estimates for the asymptotics of the visibility in the vacant set. We also consider visibility inside the vacant set of the Brownian excursion process in the unit disc and show that it undergoes a phase transition regarding visibility to infinity as in \cite{benjamini2009visibility}. Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.

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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

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