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Optimal local law and central limit theorem for $β$-ensembles
In the setting of generic $\beta$-ensembles, we use the loop equation hierarchy to prove a local law with optimal error up to a constant, valid on any scale including microscopic.
Probability Mathematical Physics Mathematical Physics
Topological Data Analysis of Decision Boundaries with Application to Model Selection
We propose the labeled \v{C}ech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks.
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