Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Airy kernel at the soft edge | Statement: [Gaussian orthogonal ensemble, scalingLimit, Airy kernel at the soft edge]

Target entity: Airy kernel at the soft edge
Context triple: [Gaussian orthogonal ensemble, scalingLimit, Airy kernel at the soft edge]

• A. Tracy–Widom distribution
  The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
• B. Wigner semicircle law
  The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
• C. Selberg integral
  The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
• D. Wigner matrices
  Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
• E. Szegő limit theorem
  The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Airy kernel at the soft edge
Target entity description: The Airy kernel at the soft edge is a universal correlation kernel describing the local eigenvalue statistics near the largest eigenvalues (soft edge) of large random matrices in ensembles such as the Gaussian orthogonal ensemble.

• A. Tracy–Widom distribution
  The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
• B. Wigner semicircle law
  The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
• C. Selberg integral
  The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
• D. Wigner matrices
  Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
• E. Szegő limit theorem
  The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
• F. None of above. chosen