Infinite-Particle Determinantal Dynamics from Brownian Motion on GLN(ℂ)
Abstract
We study the edge scaling limit of the logarithms of the squared singular values of multiplicative Brownian motion on the general linear group GLN(ℂ) with general initial conditions. Building on earlier work [arXiv:2605.06429], we prove that, for every initial condition in the enhanced state space, the limiting dynamics are determinantal and derive an explicit double-contour formula for their extended multitime correlation kernel. The dependence on the initial state, including information not determined by the particle coordinates, is encoded by the associated Laguerre--Pólya entire function. We further extend the construction of solutions to the corresponding infinite-dimensional system of singular stochastic differential equations to arbitrary initial configurations, including those with coinciding coordinates.
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BibTeX
@misc{mirsajjadi2026infiniteparticle,
title = {{Infinite-Particle Determinantal Dynamics from Brownian Motion on $\mathrmGL_N(\mathbbC)$}},
author = {Zahra Sadat Mirsajjadi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35383},
eprint = {2609.35383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35383},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Infinite-Particle Determinantal Dynamics from Brownian Motion on GL_N(ℂ)
AU - Zahra Sadat Mirsajjadi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.35383
UR - https://arxiv.org/abs/2609.35383
AB - We study the edge scaling limit of the logarithms of the squared singular values of multiplicative Brownian motion on the general linear group GL_N(ℂ) with general initial conditions. Building on earlier work [arXiv:2605.06429], we prove that, for every initial condition in the enhanced state space, the limiting dynamics are determinantal and derive an explicit double-contour formula for their extended multitime correlation kernel. The dependence on the initial state, including information not determined by the particle coordinates, is encoded by the associated Laguerre--Pólya entire function. We further extend the construction of solutions to the corresponding infinite-dimensional system of singular stochastic differential equations to arbitrary initial configurations, including those with coinciding coordinates.
ER -