Pith. Sign in

RECORD

GUE minors, maximal Brownian functionals and longest increasing subsequences

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
Florent Benaych-Georges (MAP5), Christian Houdré

Probability · Submitted 11 Dec 2013

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

The authors' main claim We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1312.3301 (version 2)
Pith IDZ5YZUR35, Pith's permanent record of this paper and its review
CitationChristian Houdr\'e, Florent Benaych-Georges (MAP5). "GUE minors, maximal Brownian functionals and longest increasing subsequences." arXiv:1312.3301 (2013). https://pith.science/paper/Z5YZUR35
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, 2,969 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.22 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover the limiting shape (properly centered and scaled) of the RSK Young diagrams associated with a random word as a function of the spectra of these minors. Since the length of the top row of the diagrams is the length of the longest increasing subsequence of the random word, the corresponding limiting law also follows.

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 present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. result 0.82 0.92 0.76 asserted 1.00
s1 In turn, these results allow to recover the limiting shape (properly centered and scaled) of the RSK Young diagrams associated with a random word as a function of the spectra of these minors. result 0.61 0.81 0.22 asserted 0.97
s2 Since the length of the top row of the diagrams is the length of the longest increasing subsequence of the random word, the corresponding limiting law also follows. interpretation 0.70 0.67 0.31 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

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 present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover the limiting shape (properly centered and scaled) of the RSK Young diagrams associated with a random word as a function of the spectra of these minors. Since the length of the top row of the diagrams is the length of the longest increasing subsequence of the random word, the corresponding limiting law also follows.

Human review

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

References
How the literature uses it

2 arXiv papers cite this in 2 sentences

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

Papers citing it · 1 sentence without a confident label

Cites it as support 1 paper
  • ζ̂^() ≡∑_i=1^γ̂_i =: γ̂The validity of this conjecture for the continuum, finite temperature model, is suggested by an argument of universality [ref] , together with exact results on discrete DP models at zero temperature, specifically the last passage percolation model [ref] and the semi-discrete directed polymer [ref] .

    Mutually avoiding paths in random media and largests eigenvalues of random matrices · Introduction · 1.00

Discussion

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