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Record W3100885978

Invasion percolation on the Poisson-weighted infinite tree

2016· article· en· W3100885978 on OpenAlex
Ross J. Kang

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueCentrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2016
Typearticle
Languageen
FieldMathematics
TopicStochastic processes and statistical mechanics
Canadian institutionsMcGill University
Fundersnot available
KeywordsCombinatoricsMathematicsPoisson distributionWeight functionPercolation (cognitive psychology)Tree (set theory)GraphDiscrete mathematicsConnected componentMathematical analysisStatistics
DOInot available

Abstract

fetched live from OpenAlex

We study invasion percolation on Aldous ’ Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the σ → ∞ limit of a representation discovered by Angel, Goodman, den Hollander and Slade [2]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it turns out that the two processes have extremely similar behavior. Finally, we introduce two new “stationary ” representations of the Poisson incipient infinite cluster as random graphs on Z which are, in particular, factors of a homogeneous Poisson point process on the upper half-plane R × [0,∞).

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.013
metaresearch head score (Gemma)0.008
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesScience and technology studies
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.906
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0130.008
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0010.001
Scholarly communication0.0010.001
Open science0.0020.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.165
GPT teacher head0.387
Teacher spread0.222 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it