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A note on the local weak limit of a sequence of expander graphs

2021
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Electronic Communications in Probability
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We show that the local weak limit of a sequence of finite expander graphs with uniformly bounded degree is an ergodic (or extremal) unimodular random graph. In particular, the critical probability of percolation of the limiting random graph is constant almost surely. As a corollary, we obtain an improvement to a theorem by Benjamini-Nachmias-Peres (2011) in [4] on locality of percolation probability for finite expander graphs with uniformly bounded degree where we can drop the assumption that

doi:10.1214/21-ecp402
fatcat:7hhwmgakafglzh7cxtwzukx4ay