Introduction to the Rapid Decay
                    property

Chatterji, Indira

doi:10.1090/conm/691/13893

Cited by 14 publications

(14 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will discuss this in greater detail in Remark 2.13. Referring to Chatterji's overview article [Cha16] about Property (RD), the following groups from Diagram (1.1) are known to enjoy it: virtually nilpotent, hyperbolic, Coxeter, CATp0q cubical, and mapping class groups (Sapir [Sap15] also wrote a nice overview article about it). To the knowledge of the author there seems to be no relation between having contractible asymptotic cones and having Property (RD).…”

Section: Related Workmentioning

confidence: 99%

Banach strong Novikov conjecture for polynomially contractible groups

Engel

2018

Advances in Mathematics

View full text Add to dashboard Cite

show abstract

Section: Related Workmentioning

confidence: 99%

Banach strong Novikov conjecture for polynomially contractible groups

Engel

2018

Advances in Mathematics

View full text Add to dashboard Cite

show abstract

“…We refer to [17] for an introduction to the RD property. We note that free groups and hyperbolic groups satisfy the RD property.…”

Section: Definition 3 (Rd Property)mentioning

confidence: 99%

Cutoff at the entropic time for random walks on covered expander graphs

Bordenave,

Lacoin

2018

Preprint

View full text Add to dashboard Cite

It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph Gn with n vertices is asymptotically bounded from below by d d−2 log n log(d−1) . Such a bound is obtained by comparing the walk on Gn to the walk on d-regular tree T d . If one can map another transitive graph G onto Gn, then we can improve the strategy by using a comparison with the random walk on G (instead of that of T d ), and we obtain a lower bound of the form 1 h log n, where h is the entropy rate associated with G. We call this the entropic lower bound. It was recently proved that in the case G = T d , this entropic lower bound (in that case d d−2 log n log(d−1) )is sharp when graphs have minimal spectral radius and thus that in that case the random walk exhibit cutoff at the entropic time. In this paper, we provide a generalization of the result by providing a sufficient condition on the spectra the random walks on Gn under which the random walk exhibit cutoff at the entropic time. It applies notably to anisotropic random walks on random d-regular graphs and to random walks on random n-lifts of a base graph.

show abstract

“…Valette's conjecture about property RD for uniform lattices in higher rang semisimple Lie groups (see [10]). In [2], Bader and Muchnik apply the Riesz-Thorin interpolation theorem and reduce their L 2 uniform bound problem to one about L ∞ norms.…”

Section: Uniform Boundedness Bounding Operator Norms Of Averages Of mentioning

confidence: 99%