9783034603317 - discrete groups, expanding graphs and invariant measures: appendix by jonathan d. rogawski (modern birkhäuser classics) von lubotzky, alex (5 Ergebnisse)
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Paperback. Zustand: Brand New. reprint edition. 192 pages. 9.00x6.00x0.25 inches. In Stock.
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Zustand: New. Unifying concepts from various fields within mathematics, this volume offers solutions to two known problems - the construction of expanding graphs and the Ruziewicz problem, concerning the finitely additive invariant measures of spheres. Series: Modern Birkhauser Classics. Num Pages: 196 pages, biography. BIC Clas…sification: PBG; PBH; PBKB; PBMP. Category: (P) Professional & Vocational. Dimension: 234 x 159 x 12. Weight in Grams: 322. . 2009. 1st ed. 1994. 2nd printing 2009. Paperback. . . . . Books ship from the US and Ireland.
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Taschenbuch. Zustand: Neu. Discrete Groups, Expanding Graphs and Invariant Measures | Appendix by Jonathan D. Rogawski | Alex Lubotzky | Taschenbuch | xi | Englisch | 2009 | Birkhäuser | EAN 9783034603317 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berl…in, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Sprache: Englisch
Verlag: Springer, Basel, Birkhäuser Verlag, Birkhäuser, 2009
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In the last fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit con…struction of expanding graphs ('expanders'). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only nitely additive measure of total measure one, de ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan's property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
