Proof of a conjecture of N. Konno for the 1D contact process
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چکیده
Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers n, m, the upper invariant measure has the following property: Conditioned on the event that O is infected, the events {All sites −n, . . . ,−1 are healthy} and {All sites 1, . . . , m are healthy} are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in [2].
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تاریخ انتشار 2006