J. Hong: An upper bound for pc in range-R bond percolation in two and three dimensions

Abstract: An upper bound for the critical probability of long range bond percolation in d=2 and d=3 is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins (2016). A key ingredient is that we establish a uniform bound for the local times of branching random walk by calculating their exponential moments and by using the discrete versions of Tanaka’s formula and Garsia’s Lemma.

arXiv: 2107.14173


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