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Record W2936365448

Uniqueness of minimizer for countable Markov shifts

2019· preprint· en· W2936365448 on OpenAlexaff
Hiroki Takahasi

Bibliographic record

VenuearXiv (Cornell University) · 2019
Typepreprint
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsUniquenessCountable setMathematicsMarkov chainAlphabetThermodynamic equilibriumApplied mathematicsFunction (biology)Statistical physicsPure mathematicsMathematical analysisThermodynamicsPhysicsStatistics
DOInot available

Abstract

fetched live from OpenAlex

We analyze large deviations rate functions for one-dimensional topological Markov shifts over infinite alphabet. We provide a sufficient condition on the potential which ensures that minimizers of the rate function are equilibrium states in the thermodynamic formalism. A combination of this result with Mauldin-Urbanski's and Sarig's uniqueness theorems of Gibbs-equilibrium states yields a version of Dobrushin-Lanford-Ruelle's variational principle: the Gibbs state, the equilibrium state, the minimizer are all unique and they coincide. A main technical ingredient is a certain {\it hidden upper semi-continuity}, first discovered by Fan-Jordan-Liao-Rams in a limited setting which we develop further and exploit. From the uniqueness of minimizer we deduce several conclusions.

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 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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.481
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
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 head0.125
GPT teacher head0.239
Teacher spread0.114 · 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 teacher head, not a consensus.

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

Citations0
Published2019
Admission routes1
Has abstractyes

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