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- W2187468988 abstract "We consider a random fleld (Xn)n2Zd and investigate when the set Ah = fk 2 Z d ;jXkj ‚ hg has inflnite clusters. The main problem is to decide whether the critical level hc = supfh2 R;P(Ah has an inflnite cluster) > 0g is nei- ther 0 nor +1. Thus, we say that a percolation transition occurs. In a flrst time, we show that weakly dependent Gaussian flelds satisfy to a well-known criterion implying the percolation transition. Then, we introduce a concept of percolation along reasonable paths and therefore prove a phenomenon of percolation transition for reasonable paths even for strongly dependent Gaussian flelds. This allows to obtain some results of percolation transition for oriented percolation. Finally, we study some Gibbs states associated to a perturbation of a ferromagnetic quadratic interaction. At flrst, we show that a transition percolation occurs for superstable potentials. Next, we go to the the critical case and show that a transition percola- tion occurs for directed percolation when d‚ 4. We also note that the assumption of ferromagnetism can be relaxed when we deal with Gaussian Gibbs measures, i.e. when there is no perturbation of the quadratic interaction." @default.
- W2187468988 created "2016-06-24" @default.
- W2187468988 creator A5007215746 @default.
- W2187468988 date "2004-01-01" @default.
- W2187468988 modified "2023-09-27" @default.
- W2187468988 title "Percolation Transition for Some Excursion Sets" @default.
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