Deformations of biorthogonal ensembles and universality
(2025) Electronic Journal of Probability — Vol. 30 (2025)
Files
EJP1409-ClaeysSilva-final.pdf
Open Access - Adobe PDF
- 383.49 KB
Details
- Authors
- Abstract
- We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal ensemble converges to a (universal) limiting process, then the deformed biorthogonal ensemble converges to a deformed version of the same limiting process. To construct the deformed version of the limiting process, we rely on a procedure of marking and conditioning. Our approach is based on an analysis of the probability generating functionals of the ensembles and is conceptually different from the traditional approach via correlation kernels. Thanks to this method, our sufficient conditions are rather mild and do not rely on much regularity of the original ensemble and of the deformation. As a consequence of our results, we obtain probabilistic interpretations of several Painlevé-type kernels that have been constructed in the literature, as deformations of classical sine and Airy point processes.
- Affiliations
Citations
Claeys, T., & Silva, G. (2025). Deformations of biorthogonal ensembles and universality. Electronic Journal of Probability, 30. https://doi.org/10.1214/25-EJP1409 (Original work published 2025)