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- W2897280385 abstract "We consider the membrane model on a box $V_Nsubset mathbb{Z}^n$ of size $(2N+1)^n$ with zero boundary condition in the subcritical dimensions $n=2$ and $n=3$. We show optimal estimates for the probability that the field is positive in a subset $D_N$ of $V_N$. In particular we obtain for $D_N=V_N$ that the probability to be positive on the entire domain is exponentially small and the rate is of the order of the surface area $N^{n-1}$." @default.
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- W2897280385 date "2018-10-11" @default.
- W2897280385 modified "2023-09-27" @default.
- W2897280385 title "Probability to be positive for the membrane model in dimensions 2 and 3" @default.
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