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arXiv · 1405.6692

Infinite Dimensional Stochastic Differential Equations for Dyson's Model

Li-Cheng Tsai
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Abstract

In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional Stochastic Differential Equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion (DBM), for all $β\geq 1$. Our construction applies to an explicit and general class of initial conditions, including the lattice configuration $\{x_i\}=\mathbb{Z}$ and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (2010) for the solution of this SDE at $β=2$.

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Li-Cheng Tsai. 2015-10-28. Infinite Dimensional Stochastic Differential Equations for Dyson's Model. https://doi.org/10.1007/s00440-015-0672-2

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