Pith. Sign in

RECORD

Extremal eigenvalue fluctuations in the GUE minor process and the law of fractional logarithm

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Elliot Paquette, Ofer Zeitouni

Probability · Submitted 21 May 2015

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

The authors' main claim We show the analogue of the law of iterated logarithm for this sequence, i.e. we divide the normalized n-th eigenvalue by a logarithmic factor and show the limsup of this sequence is a constant almost surely.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1505.05627 (version 2)
Pith IDDJ46FBUV, Pith's permanent record of this paper and its review
CitationElliot Paquette, Ofer Zeitouni. "Extremal eigenvalue fluctuations in the GUE minor process and the law of fractional logarithm." arXiv:1505.05627 (2015). https://pith.science/paper/DJ46FBUV
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,624 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.66 · compares with prior results 0.18 · 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 the GUE minor process, where a sequence of GUE matrices is drawn from the corner of a doubly infinite array of i.i.d. standard normal variables subject to the symmetry constraint. From each matrix, we take its largest eigenvalue, appropriately rescaled to converge to the standard Tracy-Widom distribution. We show the analogue of the law of iterated logarithm for this sequence, i.e. we divide the normalized n-th eigenvalue by a logarithmic factor and show the limsup of this sequence is a constant almost surely. We also give almost sure bounds for the appropriately scaled liminf.

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 GUE minor process, where a sequence of GUE matrices is drawn from the corner of a doubly infinite array of i.i.d. standard normal variables subject to the symmetry constraint. background 0.46 0.31 0.02 asserted 0.81
s1 From each matrix, we take its largest eigenvalue, appropriately rescaled to converge to the standard Tracy-Widom distribution. method 0.94 0.70 0.04 asserted 0.86
s2 We show the analogue of the law of iterated logarithm for this sequence, i.e. we divide the normalized n-th eigenvalue by a logarithmic factor and show the limsup of this sequence is a constant almost surely. result 0.94 0.96 0.86 asserted 1.00
s3 We also give almost sure bounds for the appropriately scaled liminf. result 0.95 0.94 0.09 asserted 0.99

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
levels run
  • 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 the GUE minor process, where a sequence of GUE matrices is drawn from the corner of a doubly infinite array of i.i.d. standard normal variables subject to the symmetry constraint. From each matrix, we take its largest eigenvalue, appropriately rescaled to converge to the standard Tracy-Widom distribution. We show the analogue of the law of iterated logarithm for this sequence, i.e. we divide the normalized n-th eigenvalue by a logarithmic factor and show the limsup of this sequence is a constant almost surely. We also give almost sure bounds for the appropriately scaled liminf.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.