Fall 2013

Noise Stability and Central Limit Theorem for Random Effective Resistance

Thursday, October 3rd, 2013 11:40 am12:30 pm

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We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side length n, when n goes to infinity.