Examples of mixing dynamic RE Sample Clauses

Examples of mixing dynamic RE. We give here some example of n-cone-mixing dynamic RE according to Definition 3.1. (1) Independent spin-flip dynamics (2) Space-time strong-mixing Gibbsian field and IPS in the regime M < ϵ Consider a dynamic RE ξ constituted by a space-time Gibbsian field as in the example of Section 2.4.3. As shown in [36] (see just after Eq. (2.7) therein), by requiring that the Gibbsian field ξ is strong-mixing in the sense of Definition 1.7 in [36] (see Eq. (1.9) therein), it follows that ξ is an n-cone-mixing dynamic RE. If ξ is a spin-flip system in the regime M < ϵ (see Section 2.4.1), then due to spatial correlations the argument used in (3.49) does not hold. Nevertheless, such systems are equivalent, in terms of mixing properties, to a Gibbsian field in the uniqueness regime at high temperature (see e.g. [65, 66]), and are therefore expected to satisfy the n- cone-mixing property in Definition 3.1. We plan to settle this technical issue in the future.
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