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- W2896952310 abstract "In this paper, we compare the solutions of Dyson Brownian motion with general $beta$ and potential $V$ and the associated McKean-Vlasov equation near the edge. Under suitable conditions on the initial data and potential $V$, we obtain the optimal rigidity estimates of particle locations near the edge for short time $t=text{o}(1)$. Our argument uses the method of characteristics along with a careful estimate involving an equation of the edge. With the rigidity estimates as an input, we prove a central limit theorem for mesoscopic statistics near the edge which, as far as we know, have been done for the first time in this paper. Additionally, combining with cite{LandonEdge}, our rigidity estimates are used to give a proof of the local ergodicity of Dyson Brownian motion for general $beta$ and potential at the edge, i.e. the distribution of extreme particles converges to Tracy-Widom $beta$ distribution in short time." @default.
- W2896952310 created "2018-10-26" @default.
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- W2896952310 date "2018-10-18" @default.
- W2896952310 modified "2023-09-26" @default.
- W2896952310 title "Dyson Brownian Motion for General $beta$ and Potential at the Edge" @default.
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- W2896952310 doi "https://doi.org/10.48550/arxiv.1810.08308" @default.
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