Year: 2025
Type: preprint
Abstract: We obtain Fisher-Hartwig asymptotics with root and jump type singularities in space-time under the law of the stationary Hermitian Ornstein-Uhlenbeck process, which serve as a dynamical generalization of earlier static results obtained by Riemann-Hilbert methods. This extends previous asymptotics by [Krasovsky 2007], [Its, Krasovsky 2008], and [Charlier 2019]. As a consequence, fractional powers of the absolute value of the characteristic polynomial of this process (and the exponential eigenvalues counting process) converge to a two dimensional Gaussian multiplicative chaos measure on an infinite strip in the subcritical phase. The dynamical Fisher-Hartwig asymptotics also provide the leading order of the log-characteristic polynomial, together with optimal bulk rigidity for non-intersecting Brownian motions. These results offer (i) the second connection between random matrix theory and Liouville quantum gravity measures after [Bourgade, Falconet 2025], by proving a dynamical generalization of the single-time convergence to the GMC from [Berestycki, Webb, Wong 2018], (ii) a dynamical extension of the maximum of the log-characteristic polynomial [Lambert, Paquette 2019] and the optimal rigidity [Claeys, Fahs, Lambert, Webb 2021].
Source: arXiv (Cornell University)
Author: Keles, Ahmet
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7075994185
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