Approximation of symmetrizations by Markov processes

Abstract

Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetrization. We cover several settings, including the approximation of the spherical nonincreasing rearrangement by Steiner symmetrizations, polarizations and cap symmetrizations. A key tool in our analysis is a quantitative measure of the asymmetry.

References in corpus (2)

• Explicit approximation of the symmetric rearrangement by polarizations
• Convergence in shape of Steiner symmetrizations

Cited by in corpus (2)

• Rearrangement and polarization
• Ergodic properties of folding maps on spheres