Entropy and isoperimetry for linear and non-linear group actions

51 citations recorded by the source corpus.

How researchers see this paper

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

Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups (2011, background): “Wreath products and groups resembling wreath products (see Gromov [51]) are so far the only known examples of groups with super-exponential Følner function, where we know the asymptotics of this function.”
Groups, Orders, and Dynamics (2014, unknown): “s an application of the Saloﬀ-Coste’s isoperimetric inequality [171]: If Y satisﬁes |∂GY|/|Y| ≤ 1/n, then its cardinal is greater than or equal to a half of the cardinal of a ball of radius n/2. (See [79] for an elementary proof of this inequality.) Remark1.4.26. In the example above, the group Γ no”
Milnor's Problem on the Growth of Groups and its Consequences (2011, methodology): “other asymptotic invariants has been introduced since that. The asymptotic methods in the case of algebras (including the topics of self-similarity) are discussed in survay of E.Zelmanov [198] and in [112]. The direction of asymptotic group theory is ﬂourishing at present time and there is no doubt ”