Nash-Free Functional-Analytic Proof of the CLT for Divergence-Free Random Walks
An alternative proof of the weak central limit theorem for random walks in divergence-free (doubly stochastic) random environments that removes the diagonal heat-kernel upper bound derived from Nash's inequality. The original Kozma-Toth argument coupled a Kipnis-Varadhan martingale approximation with a Nash/evolving-sets heat-kernel bound requiring strict ellipticity. This proof instead controls the antisymmetric part of the generator purely through functional-analytic estimates on the unbounded operator |L+L*|^{-1/2}(L-L*)|L+L*|^{-1/2}, so it no longer depends on ellipticity and extends to non-elliptic regimes.
CENTRAL LIMIT THEOREM FOR RANDOM WALKS IN DIVERGENCE FREE RANDOM DRIFT FIELD - REVISITED B´ALINT
A probability-theory note (Balint Toth) giving a new proof of the weak central limit theorem for continuous-time nearest-neighbour random walks in a stationary, ergodic, zero-mean divergence-free (do…