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Record W2117305637 · doi:10.1214/aop/1019160326

Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees

2000· article· en· W2117305637 on OpenAlexfundno aff
Peter Donnelly, Steven N. Evans, Klaus Fleischmann, Thomas G. Kurtz, Xiaowen Zhou

Bibliographic record

VenueThe Annals of Probability · 2000
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsnot available
FundersDivision of Mathematical SciencesEngineering and Physical Sciences Research CouncilPacific Institute for the Mathematical SciencesNational Science Foundation
KeywordsMathematicsBrownian motionHausdorff dimensionBrownian excursionMarkov processSemigroupMetric spaceRandom walkPacking dimensionMathematical analysisStatistical physicsPure mathematicsDiffusion processGeometric Brownian motionFractalMinkowski–Bouligand dimensionFractal dimension

Abstract

fetched live from OpenAlex

Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representation is obtained here in terms of a limit of interacting particle systems. It is shown that, under a mild condition on the migration process, the continuum-sites stepping-stone process has continuous sample paths. The case when the migration process is Brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating Brownian motion. This duality relation is also used to show that a tree-like random compact metric space that is naturally associated to an in .nite family of coalescing Brownian motions on the circle has Hausdorff and packing dimension both almost surely equal to 1/2 and, moreover, this space is capacity equivalent to the middle-1/2 Cantor set (and hence also to the Brownian zero set).

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.004
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
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 score0.003
Threshold uncertainty score0.009

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0010.002
Scholarly communication0.0020.003
Open science0.0010.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0030.000

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 head0.229
GPT teacher head0.355
Teacher spread0.125 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations35
Published2000
Admission routes1
Has abstractyes

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