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Discrete Groups, Expanding Graphs and Invariant Measures (1994)

Lubotzky, Alexander. ; SpringerLink 〈Online service〉

Basel :Birkhäuser Basel :

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UID:

almahu_9947363061702882

Format: XI, 196 p. , online resource.

ISBN: 9783034603324

Series Statement: Modern Birkhäuser Classics

Content: 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 construction 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.

Note: Expanding Graphs -- The Banach-Ruziewicz Problem -- Kazhdan Property (T) and its Applications -- The Laplacian and its Eigenvalues -- The Representation Theory of PGL 2 -- Spectral Decomposition of L 2(G(?)\G(A)) -- Banach-Ruziewicz Problem for n = 2, 3; Ramanujan Graphs -- Some More Discrete Mathematics -- Distributing Points on the Sphere -- Open Problems.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783034603317

Language: English

DOI: 10.1007/978-3-0346-0332-4

URL: http://dx.doi.org/10.1007/978-3-0346-0332-4

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HU Berlin

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Discrete Groups, Expanding Graphs and Invariant Measures (2010)

Lubotzky, Alexander 1956- ; Rogawski, Jonathan D.

Basel : Birkhäuser Basel

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UID:

gbv_632390999

Format: Online-Ressource , v.: digital

Edition: Reprint of the 1994 ed.

Edition: Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web

ISBN: 9783034603324

Series Statement: Modern Birkhäuser Classics

Note: "Reprint of the 1994 edition , Includes bibliographical references and index , Electronic reproduction; Available via World Wide Web

Additional Edition: ISBN 9783034603317

Additional Edition: Erscheint auch als Druck-Ausgabe Lubotzky, Alexander, 1956 - Discrete groups, expanding graphs and invariant measures Basel : Birkhäuser, 1994 ISBN 376435075X

Additional Edition: ISBN 081765075X

Language: English

Subjects: Mathematics

RVK:

SK 180

RVK:

SK 340

Keywords: Lie-Gruppe ; Expandierender Graph ; Invariantes Maß

DOI: 10.1007/978-3-0346-0332-4

URL: Volltext (lizenzpflichtig)

URL: Inhaltstext

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UB Potsdam

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Discrete groups, expanding graphs and invariant measures (2010)

Lubotzky, Alexander

Basel [u.a.] : Birkhäuser

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UID:

kobvindex_ZLB15115150

Format: XI, 192 Seiten , graph. Darst.

Edition: [Nachdr.]

ISBN: 9783034603317

Series Statement: Modern Birkhäuser classics

Note: Nachdr. der Ausg. Basel 1994 , Text engl.

Language: English

Keywords: Lie-Gruppe ; Expandierender Graph ; Invariantes Maß

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Berlin VÖBB/ZLB

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Discrete groups, expanding graphs and invariant measures (1994)

Lubotzky, Alexander [Verfasser]

Basel [u.a.] : Birkhäuser

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UID:

b3kat_BV036568187

Format: 1 Online-Ressource

Edition: Reprint of the 1994 ed.

ISBN: 9783034603317 , 3034603312 , 9783034603324 , 3034603320

Series Statement: Modern Birkhäuser classics

Language: English

Subjects: Mathematics

RVK:

SK 180

RVK:

SK 340

Keywords: Lie-Gruppe ; Expandierender Graph ; Invariantes Maß

DOI: 10.1007/978-3-0346-0332-4

URL: Volltext

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BTU Cottbus

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Discrete groups, expanding graphs and invariant measures (2010)

Lubotzky, Alexander [Verfasser] ; Rogawski, Jonathan D.

Basel [u.a.] : Birkhäuser

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UID:

b3kat_BV035834550

Format: XI, 192 S.

Edition: Reprint of the 1994 ed.

ISBN: 9783034603317 , 9783034603324

Series Statement: Progress in mathematics 125

Language: English

Subjects: Mathematics

RVK:

SK 340

Keywords: Lie-Gruppe ; Expandierender Graph ; Invariantes Maß

URL: Inhaltsverzeichnis

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TU Berlin

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Discrete groups, expanding graphs and invariant measures / (2010)

Lubotzky, Alexander ; Rogawski, Jonathan D.

Basel [u.a.] :Birkhäuser,

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UID:

almafu_BV026925188

Format: XI, 192 S.

Edition: Reprint of the 1994 ed.

ISBN: 978-3-0346-0331-7 , 978-3-0346-0332-4

Series Statement: Modern Birkhäuser Classics

Language: English

Subjects: Mathematics

RVK:

SK 340

Keywords: Lie-Gruppe ; Expandierender Graph ; Invariantes Maß

URL: Inhaltsverzeichnis

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022448177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

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