Uma versão quantitativa do Teorema de Grimmett-Marstrand - Célio Augusto Terra de Souza (2020)
In whis work we present a recent result by H. Duminil-Copin, G. Kozma and V. Tassion, giving an upper bound for the critical percolation parameter in slabs. Through a renormalization scheme coupled with an exploratory process, we prove that p_c(Slab_n^d)=p_c+O(1/\sqrt{log n})$. Using this bound we show an upper bound for the correlation length $\xi_p$, concluding that $\xi_p \le \exp(C(p-p_c)^{-2})$ for some constant $C$ large enough.