OpenFrontiers
Join
← Back to the index
OP-8067Status unassessedAnalysis

Random Matrix Theory · Question 1

Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

Study the expansion of partition functions of normal matrix models for

v(z,z‾)=(zz‾)d−t(zd+z‾d)v(z,\overline{z})=(z \overline{z})^d-t(z^d+\overline{z}^d)

and

zN=C(d,N)∏l=0d−1EGin{∣det(MGin−z)∣γl},z_N=C(d,N)\prod_{\mathscr{l}=0}^{d-1} \mathbb{E}_{\text{Gin}}\Big\{\Big|\text{det}(M_{\text{Gin}}-z)\Big|^{\gamma_{\mathscr{l}}}\Big\},

where z=tdz=t\sqrt{d}. Study the "mad criticality" that happens here.

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Background

Question context

Please see Alfredo Dea~{n}o and Nick Simm's article "Characteristic polynomials of complex random matrices and Painlev`{e} transcendents" for background on this problem.

Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

The source supplies no status note for this question.

References
  1. [1]Riemann-Hilbert problems, Toeplitz matrices, and applications link

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.