Dynamic theory of growth in groups: Entropy, boundaries, examples

By Anatoly M. Vershik. 2000

127 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d0444c3f7ff0a415e775c38025c02086b59f9c5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. A. Erschler
2. David Revelle
3. Alexander I. Bufetov
4. Anatoly M. Vershik
5. Rostislav I. Grigorchuk
6. C. Anantharaman-Delaroche
7. Laurent Bartholdi
8. Pablo Shmerkin

In Geometry and Topology

1. A. Erschler
2. David Revelle
3. Alexander I. Bufetov
4. Anatoly M. Vershik
5. Rostislav I. Grigorchuk
6. Misha Gromov
7. Laurent Bartholdi
8. C. Anantharaman-Delaroche

In Mathematical Physics

1. A. Erschler
2. Alexander I. Bufetov
3. David Revelle
4. Anatoly M. Vershik
5. Rostislav I. Grigorchuk
6. C. Anantharaman-Delaroche
7. Laurent Bartholdi
8. Pablo Shmerkin

Citations in the corpus

• Asymptotic entropy and Green speed for random walks on countable groups (2006, unknown): “3), when the speed and volume growth are computed in a word metric, is proved by Guivarc’h [15] and discussed in great detail by Vershik [24].”
• RATE OF ESCAPE OF RANDOM WALKS ON WREATH PRODUCTS AND RELATED GROUPS (2003, background): “Vershik [22] has written a detailed survey that covers this subject.”
• Geometry and dynamics of admissible metrics in measure spaces (2012, background): “The corresponding growth (in n, for small ε) is determined by the so-called scaling sequence, and if the numerical limit does exist, then it is called the scaling entropy, see [11].”
• Kantorovich Metric: Initial History and Little-Known Applications (2005, background): “The last formulation also motivates the definition of the so-called secondary entropy of a stationary process (see [ 24 ]).”
• Harmonic measures versus quasiconformal measures for hyperbolic groups (2008, unknown): “A.Vershik suggested the study of the case of equality (see [16, 43 ]).”
• Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization (2003, unknown): “, see the recent paper [54] and the references therein).”
• Convergence of spherical averages for actions of free groups (2002, background): “For example, this takes place for Vershik’s locally finite groups [23].”
• Liouville property for groups and manifolds (2004, background): “The non-triviality of the boundary for any measure with a finite support on Metd (d ≥ 3) was proved by A.M. Vershik in [ 37 ].”