One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 1, pp. 83-112. 
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     number = {1},
     year = {1997},
     mrnumber = {1440257},
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     url = {http://archive.numdam.org/item/AIHPB_1997__33_1_83_0/}
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Pruss, Alexander R. One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 1, pp. 83-112. http://archive.numdam.org/item/AIHPB_1997__33_1_83_0/

[1] A. Baernstein Ii, A unified approach to symmetrization, Partial Differential Equations of Elliptic Type, A. ALVINO, et al., Eds. Symposia Mathematica, Cambridge University Press, Cambridge, Vol. 35, 1994, pp. 47-91. | MR | Zbl

[2] A. Baernstein Ii, Integral means, univalent functions and circular symmetrization, Acta Math., Vol. 133, 1974, pp. 139-169. | MR | Zbl

[3] C. Borell, An inequality for a class of harmonic functions in n-space (Appendix) The cosπλ theorem, Lecture Notes in Mathematics, Springer-Verlag, New York, Vol. 467, 1975. | MR

[4] M. Essén, A theorem on convex sequences, Analysis, Vol. 2, 1982, pp. 231-252. | MR | Zbl

[5] M. Essén, The cosπλ theorem, Lecture Notes in Mathematics, Springer-Verlag, New York, Vol. 467, 1975. | MR | Zbl

[6] K. Haliste, Estimates of harmonic measures, Ark. Mat., Vol. 6, 1965, pp. 1-31. | MR | Zbl

[7] G.H. Hardy and J.E. Littlewood, Notes on the theory of series (VIII): an inequality, J. Lond. Math. Soc., Vol. 3, 1928, pp. 105-110. | JFM

[8] G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1964.

[9] A.R. Pruss, Radial rearrangement, harmonic measures and extensions of Beurling's shove theorem, Preprint, 1966.

[10] A.R. Pruss, Discrete harmonic measure, Green's functions and symmetrization: a unified probabilistic approach, Preprint, 1996.

[11] J.R. Quine, Symmetrization inequalities for discrete harmonic functions, Preprint.