The Lamplighter Group as a Group Generated by a 2-state Automaton, and its Spectrum
By Rostislav I. Grigorchuk, A. Zuk. 2001
267 citations recorded by the source corpus.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f7d7703a8358ca72522a1a23d477a1c752435136
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Volodymyr V. Nekrashevych
- Laurent Bartholdi
- Wolfgang Woess
- Thomas Schick
- Yair Glasner
- Alexander Teplyaev
- Warren Dicks
- Markus Neuhauser
In Statistics and Probability
- Thomas Schick
- Volodymyr V. Nekrashevych
- Yair Glasner
- Warren Dicks
- Laurent Bartholdi
- Wolfgang Woess
- Shahar Mozes
- Russell Lyons
Citations in the corpus
- Automata and Square Complexes (2003, methodology): “the lamplighter group) were realized as groups of type GðAÞ, giving rise to new understanding of their properties [9, 11 ].”
- The Spectral Measure of Certain Elements of the Complex Group Ring of a Wreath Product (2001, methodology): “In particular, we give a transparent explanation of the spectral measure of the Markov operator on the lamplighter group found by Grigorchuk-Zuk [4].”
- Self-Similarity, Operators and Dynamics (2003, background): “Graphs of certain fractal groups studied in [1, 5, 6] have a fractal spectrum, although they seem to be different from the graphs considered here.”
- ON RANDOM WALKS ON WREATH PRODUCTS (2002, unknown): “Wreath products also appear in recent works by Erschler (Dyubina) [13, 14], Grigorchuck and Żuk [18] and Revelle [41, 42].”
- Dead end words in lamplighter groups and other wreath products (2003, background): “We then describe an interesting phenomenon which occurs in this Cayley graph, namely the existence of dead end elements.”
- Horocyclic products of trees (2006, background): “[20] Grigorchuk, R. I., and Żuk, A.: The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geom.”
- Amenability of linear-activity automaton groups (2009, unknown): “See Grigorchuk and Żuk (2001).”
- CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS (2004, methodology): “Zuk and L. Bartholdi to compute the spectra of random walks on the Cayley graphs and on the Schreier graphs of the respective self-similar groups (see [ 17 ], [2]).”