Publications [#316608] of James H. Nolen

Papers Published

1. Gloria, A; Nolen, J, A Quantitative Central Limit Theorem for the Effective Conductance on the Discrete Torus, Communications on Pure and Applied Mathematics, vol. 69 no. 12 (2015), pp. 2304-2348, WILEY, ISSN 0010-3640 [cpa.21614], [doi]
   (last updated on 2024/04/19)

   Abstract:
   We study a random conductance problem on a d-dimensional discrete torus of size L > 0. The conductances are independent, identically distributed random variables uniformly bounded from above and below by positive constants. The effective conductance AL of the network is a random variable, depending on L, that converges almost surely to the homogenized conductance Ahom. Our main result is a quantitative central limit theorem for this quantity as L → ∞. In particular, we prove there exists some σ > 0 such that dK (Ld/2A – Ahom/ σ, g) ≲ L–d/2 logd L,where dK is the Kolmogorov distance and gis a standard normal variable. The main achievement of this contribution is the precise asymptotic description of the variance of AL.© 2015 Wiley Periodicals, Inc.