One-sided continuity properties for the Schonmann projection
| Autor: | Stein Andreas Bethuelsen, Diana Conache |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
010102 general mathematics Probability (math.PR) Statistical and Nonlinear Physics Monotonic function Coupling (probability) 01 natural sciences Measure (mathematics) 010104 statistics & probability symbols.namesake Mixing (mathematics) Projection (mathematics) 60K35 60E15 60K37 symbols FOS: Mathematics Almost surely Ising model 0101 mathematics Gibbs measure Mathematical Physics Mathematics - Probability Mathematics |
| Popis: | We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In $1989$ Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open. In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular $g$-measure. That is, it does possess the corresponding one-sided notion of almost Gibbsianness. We further deduce strong one-sided mixing properties which are of independent interest. Our proofs make use of classical coupling techniques and some monotonicity properties which are known to hold for one-sided, but not two-sided conditioning for FKG measures. 19 pages |
| Databáze: | OpenAIRE |
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