[A] The Concept of Concentration; Concentration Phenomenon |

[32], [33], [41], [42], [43], [49], [51], [55], [57], [61], [65],
[75], [79], [86], [128], [132], [135], [139], [148] Some crucial papers: |
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[32] | 1971, (but the talk on it was already in 1968 on Voronez winter School) - the start of the method of Concentration. | |

[33] | 1971, - it was realized here that Concentration is a general concept and not a particular property of the sphere, or its local perturbation; examples of Stiefeld and Grassmanian manifolds. | |

[43] | 1977, joint with Figiel and Lindenstrauss - far reaching development of the method in the Local Theory; the method was generally accepted after this paper. | |

[49] | 1980, joint with Amir - the method was extended to cover other metric probability spaces, including product spaces. The start of the concentration method in the Combinatorial setting. | |

[51] | 1983, joint with Gromov (but it was submitted in 1979 and lost by the journal after it was accepted); - a general setting for the Theory of Concentration; a lot of additional examples; the role of Ricci curvature and of the first non-trivial eigenvalue of the Laplacian. | |

[61] | 1985, joint with Alon - (first published at 1984 in [55] with a different introduction, emphasizing Concentration Phenomenon and in the Proceedings [62], 1984); first application of them Concentration Phenomenon to Combinatorics and Computer Science (expanders) | |

[65] | 1986, joint with Schechtman - the first book with the main emphasize on the method of Concentration and its application in the Asymptotic Theory. | |

[75] | 1987, joint with Gromov - a general setting for exact isoperimetric inequalities on the sphere with different metrics and measures; the "localization" technique is introduced. | |

[86] | 1988, - The survey on the state of knowledge at 1988 on the concepts of Concentration and Spectrum. Introducing the notion of Concentration for Infinite dim. setting without any measure {the next 10 + years I did not work in this direction} | |

[128], [132] | 2000, joint with Giannopoulos; introducing different forms of Concentration; (for metric spaces without measure, and for measure spaces without a metric). | |

Some related papers
and Books: M.Talagrand, A new look at independence. Ann. Probab. 24 (1996), no. 1, 1--34. M.Talagrand, Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Etudes Sci. Publ. Math. No. 81 (1995), 73--205 M.Ledoux, The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. M.Gromov, Metric structures for Riemannian and non-Riemannian spaces. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates. Progress in Mathematics, 152. Birkhauser Boston, Inc., Boston, MA, 1999. xx+585 pp. V.Pestov, Amenable representations and dynamics of the unit sphere in an infinite-dimensional Hilbert space. Geom. Funct. Anal. 10 (2000), no. 5, 1171--1201. |
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