Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 42 min ago
PreprintarXiv licencearXiv

Hives from deformed GUE minor processes

  • Hariharan Narayanan
Open at sourcePDFDOICite

Abstract

We construct random hives from deformed GUE minor processes. Starting from two independent diagonally deformed GUE matrices X=√n(wG+uD), Y=√n(w'G'+u'D'), where D,D' are diagonal and have GUE spectra, we use their minor processes to form a double hive and then apply the octahedron recurrence. Under the matching condition u/w2=u'/(w')2, we prove that the resulting hive law is close, in relative entropy, to a GUE hive law. More precisely, if a2=w2+u2, b2=(w')2+(u')2, then the produced hive density qn satisfies DKL ( qn middle| Density(Hn(a√n,b√n,c**√n)) ) = O(nlog n). The third scale c** is determined by a limiting tetrahedral optimization problem; equivalently, writing δ=u+u', δ2 = ( 2c**4(c**2−a2−b2) )/( (c**2−a2+b2)(c**2+a2−b2) ). Thus the construction realizes GUE hive laws, up to subleading relative entropy, throughout the right-angled and obtuse regime. The introduction records two explicit surface-tension approximations and numerical comparisons which motivated the construction.

Related

  1. q-deformed polyanalytic Ginibre point processes:construction and central limit theorems for linear statistics
    Yeong-Gwang Jung, Ryosuke Sato
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  2. An integral representation of eigenfunctions for the deformed Noumi--Sano operators
    Taikei Fujii, Takahiko Nobukawa
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  3. Unavoidable flats in matroids excluding a uniform minor
    Wayne Ge
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. Quasi-Fuchsian groups and complex realisations of q-deformed real numbers
    Alex Elzenaar
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  5. Lattice paths on snake graphs for q-deformed rationals
    Jérôme Germoni
    HALPreprintCC BY-NC-ND 4.0Full textCombinatorics & discrete mathematicsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{narayanan2026hives,
  title = {{Hives from deformed GUE minor processes}},
  author = {Hariharan Narayanan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.04138},
  eprint = {2607.04138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.04138},
}
RIS
TY  - UNPB
TI  - Hives from deformed GUE minor processes
AU  - Hariharan Narayanan
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2607.04138
UR  - https://arxiv.org/abs/2607.04138
AB  - We construct random hives from deformed GUE minor processes. Starting from two independent diagonally deformed GUE matrices X=√n(wG+uD), Y=√n(w'G'+u'D'), where D,D' are diagonal and have GUE spectra, we use their minor processes to form a double hive and then apply the octahedron recurrence. Under the matching condition u/w^2=u'/(w')^2, we prove that the resulting hive law is close, in relative entropy, to a GUE hive law. More precisely, if a^2=w^2+u^2, b^2=(w')^2+(u')^2, then the produced hive density q_n satisfies D_KL ( q_n middle| Density(H_n(a√n,b√n,c_**√n)) ) = O(nlog n). The third scale c_** is determined by a limiting tetrahedral optimization problem; equivalently, writing δ=u+u', δ^2 = ( 2c_**^4(c_**^2−a^2−b^2) )/( (c_**^2−a^2+b^2)(c_**^2+a^2−b^2) ). Thus the construction realizes GUE hive laws, up to subleading relative entropy, throughout the right-angled and obtuse regime. The introduction records two explicit surface-tension approximations and numerical comparisons which motivated the construction.
ER  -