Geodesic
Asymptotic formula for correlation decay in the stochastic model of planar rotators at high temperatures
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 67-80 
E. A. Zhizhina. Asymptotic formula for correlation decay in the stochastic model of planar rotators at high temperatures. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 67-80. http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a2/
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     title = {Asymptotic formula for correlation decay in the stochastic model of planar rotators at high temperatures},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a2/}
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We found the asymptotic formula for correlations decay $\langle f_A(x(0)),g_{A+k(t)}(x(t))\rangle$, when $t\to\infty$, $k(t)\to\infty$, $k(t)\in Z^d$, in the stochastic model of planar rotators on a lattice $x(t)=\bigl\{x_k(t),k\in Z^d\bigr\}$, $t\geq0$, $x_k(t)\in T^1$ at high temperatures. The basic methods we use are the spectral analysis of the Markov semigroup generator and the saddle-point method.

[1] R. A. Minlos, Markov Processes and Related Fields, 2:2 (1996), 263 | MR | Zbl

[2] Yu. G. Kondratiev, R. A. Minlos, J. Stat. Phys (to appear) | MR | Zbl

[3] V. A. Malyshev, R. A. Minlos, Lineinye operatory v beskonechnochastichnykh sistemakh, Nauka, M., 1994 | MR

[4] R. A. Minlos, E. A. Zhizhina, J. Stat. Phys., 84:1/2 (1996), 85 | DOI | MR | Zbl

[5] S. Albeverio, Yu. G. Kondratiev, M. Rockner, J. Funct. Anal., 133 (1995), 10 | DOI | MR | Zbl

[6] R. Holley, D. Stroock, J. Funct. Anal., 42 (1981), 29 | DOI | MR | Zbl

[7] M. V. Fedoryuk, Metod perevala, Nauka, M., 1977 | MR