Approximation of symmetrizations by Markov processes

Van Schaftingen, Jean;Dekeyser, Justin
(2017) Indiana University Mathematics Journal — Vol. 66, p. 1145-1172 (2017)

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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.
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Van Schaftingen, J., & Dekeyser, J. (2017). Approximation of symmetrizations by Markov processes. Indiana University Mathematics Journal, 66, 1145-1172. https://doi.org/10.1512/iumj.2017.66.6118 (Original work published 2017)