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In the last few years, I got interested by random tilings. One considers tiling by lozenges of a given domain given at random and wants to understand how it looks like when the mesh of the domain goes to zero. These tilings are in many respect similar to random matrices as they are very rigid, and in fact in good cases the distribution of the positions of tiles is similar to that of the eigenvalues of random matrices, except that they live on a discrete lattice. Thanks to equations inspired from the work of N. Nekrasov, we could extend ideas coming from the analysis of random matrices to this discrete setting with A. Borodin and V. Gorin [25]. We could also obtain local estimates to derive fluctuations of the boundary of the liquid region with Huang [48]. Recently, I worked on large deviations for Wigner matrices with sub-Gaussian entries [50, 3]. We introduced a new idea based on tilting the measure via spherical integrals. I expect this new line of research to be fruitful, and followed it in a few works [51, 21, 49, 7].
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arxiv(2024)
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arXiv (Cornell University) (2023)
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arxiv(2023)
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Journal of Functional Analysisno. 11 (2023): 110144-110144
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