Year: 2026
Type: preprint
Abstract: We study the Christoffel transformation $w(x)\mapsto x^2w(x)$ of an even discrete weight. For the associated orthogonal polynomial ensembles on squared nodes $y=x^2$, ratios of moment determinants relate the largest-particle distributions and transfer exact gap probability recurrences between the ensembles. For positive weights satisfying the stated moment and support assumptions, this comparison requires no Pearson condition. The transformation is realized by elementary bundle modifications at zero and infinity on $\mathbb P^1$. When the original weight has Pearson ratio $d(-z-1)/d(z)$ with $\mathrm{deg}\; d=1,2$, these modifications conjugate cutoff dynamics on common stable loci of symmetric $d$-connections under the stated geometric hypotheses. The transformed recurrence coefficients are expressed explicitly as rational functions of spectral coordinates. On the unit lattice, a local recurrence formula applies to rational symmetric Pearson ratios of arbitrary degree, including outside these charts, whenever its local hypotheses hold.
Source: arXiv (Cornell University)
Author: Selemenchuk, Anton
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6444257319, G6836815800
OpenAlex ID: W7223097362