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Date : 1994-08-01
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Discrete Groups Expanding Graphs and Invariant Measures ~ And the mathematics in Discrete Groups Expanding Graphs and Invariant Measures is nothing short of delectable including an explication of invariant measures starting with the BanachTarski paradox a crisp account of the representation theory surrounding Kazhdan’s property T leading already on p 30 ff to a solution à la Margulis of the expander construction problem — existence is “easy” see p 5 and leading to a solution of the Banach Ruziewicz problem in dimensions
Discrete Groups Expanding Graphs and Invariant Measures ~ It is therefore so what surprising that both problems were solved using similar methods initially Kazhdan’s property T from representation theory of semisimple 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
Discrete Groups Expanding Graphs and Invariant Measures ~ Discrete Groups Expanding Graphs and Invariant Measures Authors Lubotzky Alex 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 dened on the Lebesgue subsets of the ndimensional sphere and invariant under
Progress Mathematics Springer ~ and the other in measure theory were solved by amazingly similar techniques from representation theory and from analytic number theory One problern is the ex plicit construction of expanding graphs «expanders» These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit con
Discrete groups expanding graphs and invariant measures ~ Expanding Graphs The BanachRuziewicz Problem Kazhdan Property T and its Applications The Laplacian and its Eigenvalues The Representation Theory of PGL 2 Spectral Decomposition of L 2GGA BanachRuziewicz Problem for n 2 3 Ramanujan Graphs Some More Discrete Mathematics Distributing Points on the Sphere Open Problems
Discrete Groups Expanding Graphs and Invariant Meas ~ It is therefore so what surprising that both problems were solved using similar methods initially Kazhdan s property T from representation theory of semisimple 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
Discrete groups expanding graphs and invariant measures ~ Get this from a library Discrete groups expanding graphs and invariant measures Alexander Lubotzky
An application of Ramanujan graphs to C∗algebra tensor ~ Lubotzky Discrete groups expanding graphs and invariant measures Progress in Mathematics vol 125 Birkhiuser Basel 1994 17 M Morgenstern Existence and explicit constructions of q 1 regular Ramanujan graphs for every prime power q J Combin
Expansion Properties of Cayley Graphs of the Alternating ~ Expansion Properties of Cayley Graphs of the Alternating Groups Local expansion of vertex transitive graphs and random generation of finite groups Proc 23rd Annual ACM STOC 1991 164 174 Expanding Graphs and Invariant Measures Progress in Math 125 Birkhäuser Basel 1994
Kazhdans property T Wikipedia ~ Discrete groups Historically property T was established for discrete groups Γ by embedding them as lattices in real or padic Lie groups with property T There are now several direct methods available
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