Open Access
2023 Large deviations for Ablowitz-Ladik lattice, and the Schur flow
Guido Mazzuca, Ronan Memin
Author Affiliations +
Electron. J. Probab. 28: 1-29 (2023). DOI: 10.1214/23-EJP941


We consider the Generalized Gibbs ensembles of the Ablowitz-Ladik lattice and of the Schur flow. We derive large deviations principles for the distribution of the empirical measures for these ensembles. As a consequence, we deduce their almost sure convergence. Moreover, we are able to characterize their limits in terms of the equilibrium measure of the Circular, and the Jacobi beta ensemble, respectively.

Funding Statement

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while G.M. participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 20-21 semester "Universality and Integrability in Random Matrix Theory and Interacting Particle Systems". G.M. has received funding from the European Union’s H2020 research and innovation programme under the Marie Skłodowska–Curie grant No. 778010 IPaDEGAN. R.M. has received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (grant agreement No. 884584).


We thank the two anonymous referees for their comments and suggestions.


Download Citation

Guido Mazzuca. Ronan Memin. "Large deviations for Ablowitz-Ladik lattice, and the Schur flow." Electron. J. Probab. 28 1 - 29, 2023.


Received: 10 January 2022; Accepted: 27 March 2023; Published: 2023
First available in Project Euclid: 12 April 2023

MathSciNet: MR4574482
zbMATH: 07707086
Digital Object Identifier: 10.1214/23-EJP941

Primary: 15A52 , 37A50 , 37J35 , 82B05

Keywords: Ablowitz-Ladik lattice , integrable systems , Large Deviations Principle , Schur flow

Vol.28 • 2023
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