98-198 Spohn, H.

Dyson's Model of Interacting Brownian Motions at Arbitrary Coupling Strength (30K, LaTex) Mar 15, 98

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Abstract. For Dyson's model of Brownian motions we prove that the fluctuations are of order one and, in a scaling limit, are governed by an infinite dimensional Ornstein-Uhlenbeck process. This extends a previous result valid only at the free Fermion point $\beta = 2$. Dyson's model can also be interpreted as a random surface. Our result implies that the surface statistics is governed by a massless Gaussian field in the scaling limit.

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