One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Pruss, Alexander R.
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997), p. 83-112 / Harvested from Numdam
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Publié le : 1997-01-01
@article{AIHPB_1997__33_1_83_0,
     author = {Pruss, Alexander R.},
     title = {One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {33},
     year = {1997},
     pages = {83-112},
     mrnumber = {1440257},
     zbl = {0870.60066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1997__33_1_83_0}
}

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) pp. 83-112. http://gdmltest.u-ga.fr/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 1297773 | Zbl 0830.35005

[2] A. Baernstein Ii, Integral means, univalent functions and circular symmetrization, Acta Math., Vol. 133, 1974, pp. 139-169. | MR 417406 | Zbl 0315.30021

[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 466587

[4] M. Essén, A theorem on convex sequences, Analysis, Vol. 2, 1982, pp. 231-252. | MR 732333 | Zbl 0494.26008

[5] M. Essén, The cosπλ theorem, Lecture Notes in Mathematics, Springer-Verlag, New York, Vol. 467, 1975. | MR 466587 | Zbl 0335.31001

[6] K. Haliste, Estimates of harmonic measures, Ark. Mat., Vol. 6, 1965, pp. 1-31. | MR 201665 | Zbl 0178.13801

[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 54.0226.02

[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.