Transport Maps for β-Matrix Models and Universality
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Author(s)
Figalli, Alessio
Bekerman, Florent
Guionnet, Alice
Date Issued
May 2015
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Bekerman, F., A. Figalli, and A. Guionnet. “Transport Maps for $${\beta}$$ β -Matrix Models and Universality.” Communications in Mathematical Physics 338, no. 2 (May 12, 2015): 589–619.
Version
Author's final manuscript
Abstract
We construct approximate transport maps for non-critical β-matrix models, that is, maps so that the push forward of a non-critical β-matrix model with a given potential is a non-critical β-matrix model with another potential, up to a small error in the total variation distance. One of the main features of our construction is that these maps enjoy regularity estimates that are uniform in the dimension. In addition, we find a very useful asymptotic expansion for such maps which allows us to deduce that local statistics have the same asymptotic behavior for both models.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-015-2384-y
