PreprintCC BY 4.0arXiv
On some stochastic evolutions on Laguerre-Polya functions
Abstract
We prove uniqueness in law for three stochastic evolutions on normalised Laguerre-Pólya functions arising as scaling limits of matrix characteristic polynomial dynamics. In particular, this implies that Ahn's universal Brownian Gibbs line ensemble arising from random matrix products has the law of the logarithms of the reciprocal zeros of the solution, unique in law, to a simple stochastic equation on entire functions started from e−z. The method of proof relies on some integrable structure of the problem in the special form of a new duality with finite-dimensional diffusions which is closely related to intertwinings.
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BibTeX
@misc{assiotis2026some,
title = {{On some stochastic evolutions on Laguerre-Polya functions}},
author = {Theodoros Assiotis and Fengyi Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08073},
eprint = {2611.08073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08073},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On some stochastic evolutions on Laguerre-Polya functions
AU - Theodoros Assiotis
AU - Fengyi Li
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08073
UR - https://arxiv.org/abs/2611.08073
AB - We prove uniqueness in law for three stochastic evolutions on normalised Laguerre-Pólya functions arising as scaling limits of matrix characteristic polynomial dynamics. In particular, this implies that Ahn's universal Brownian Gibbs line ensemble arising from random matrix products has the law of the logarithms of the reciprocal zeros of the solution, unique in law, to a simple stochastic equation on entire functions started from e^−z. The method of proof relies on some integrable structure of the problem in the special form of a new duality with finite-dimensional diffusions which is closely related to intertwinings.
ER -