Mesoscopic fluctuations for orthogonal polynomial ensembles have been studied in the literature since 2000. However, most works focus on the bulk, and less is known about the edges. In this talk, I am reporting on my work on the mesoscopic edge universality of orthogonal polynomial ensembles arXiv:2501.14422. I will present the main theorems and the ideas of the proof with an example of Laguerre Unitary Ensemble (LUE). The interesting aspect of LUE is that it presents both hard and soft edges. Our approach reveals how the different types of edges of LUE affect the mesoscopic fluctuations. Universality comes naturally from our approach. The main tool used in this study is the Jacobi operator of the associated orthogonal polynomials. For the purpose of our analysis, we develop a Combes-Thomas type estimate for the spectral edges.

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