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The mathematical study of ensembles of random matrices (especially Hermitian ensembles such as GUE, GOE, GSE): eigenvalue distributions, spacing and correlation statistics, universality, and applications of these statistics to other systems. Claims about matrix-ensemble eigenvalue statistics belong here; claims about zeta zeros stay under their own tags.

The spacing statistics of the zeros of the Riemann zeta function match those of eigenvalues of random Hermitian matrices.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Number theory Montgomery–Odlyzko conjectureimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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