Dyson's Model of Interacting Brownian Motions at Arbitrary Coupling Strength

H. Spohn

1998, v.4, Issue 4, 469-661


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.

Keywords: interacting diffusions,random surfaces,massless Gaussian field


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