Dynamics of a spin-exchange model
The studied spin-exchange models are motivated by the investigation of the behaviour of a non-equilibrium interface introduced in the Toom model. Its approximations were studied by \textit{B. Derrida, J. L. Lebowitz, E. R. Speer} and \textit{H. Spohn} [J. Phys. A, Math. Gen. 24, No. 20, 4805-4834 (1991; Zbl 0759.60104)] using computer simulations. Here, the authors study the first approximation of Derrida at al. rigorously and they confirm the former observation concerning the typical size of a flat part of the interface anchored at the origin in dependence on the distance from the origin. The model is an ``annihilating random walk on \(\mathbb Z_0^+\) with co-jumping of two neighbours and source at the origin'' \(\eta _t^c\subset \mathbb Z_0^+\) for \(t\in [0,\infty )\). (We omit here the exact description.) It is shown that \(\lim _{x\to \infty } 2\sqrt {\pi x} P(x\in \eta _\infty ^c)=1.\) The same result is obtained also for the ``annihilating random walk'', where the simultaneous co-jumping of two neighbours does not occur. Coalescing random walk and asymmetric voter model are employed in the proofs, and a duality of them is used.
scientific article; zbMATH DE number 1109421
scientific article