Asymptotic formula for the decay of correlations in the stochastic model of planar rotators at high temperature
We consider the stochastic model of planar rotators \(x(t)=\{x_k(t),\;k\in Z^d\}\), \(t\geq 0\), \(x_k(t)\in T^1\), at high temperature. For the decay of correlations \(\langle f_A(x(0)),g_{A+k(t)}(x(t))\rangle\), the asymptotic formula is obtained at \(t\to\infty\), \(k(t)\to\infty\), \(k(t)\in Z^d\). The basic methods we use are the spectral analysis of the Markov semigroup generator and the saddle-point method.
scientific article; zbMATH DE number 1324754