10 citations · 11 across the 6 of their papers we have counts for
7 papers
Relative (), Expanders, and Decay of Correlations for certain Expanding Maps
Rhiannon Dougall
Relative () is equivalent to a statement that the sequence of Cayley graphs associated to group quotients , , form an expander family. There is a phil…
A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups
Rhiannon Dougall, Richard Sharp
We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is…
Discrete group extensions of countable Markov shifts and pressure gap
Rhiannon Dougall
The main outcome of this note is to extend the work of Stadlbauer (\textit{An extension of Kesten's criterion for amenability to topological Markov chains}, 2013), Coulon--Dal'Bo--…
Anosov flows, growth rates on covers and group extensions of subshifts
Rhiannon Dougall, Richard Sharp
The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions…
Twisted Patterson-Sullivan measures and applications to amenability and coverings
Rémi Coulon, Rhiannon Dougall, Barbara Schapira +1
Let be two discrete groups acting properly by isometries on a Gromov-hyperbolic space . We prove that their critical exponents coincide if and only if is co-amenable…
Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance
Rhiannon Dougall
For a pinched Hadamard manifold and a discrete group of isometries of , the critical exponent is the exponential growth rate of the orbit of a point in under t…
Amenability, Critical Exponents of Subgroups and Growth of Closed Geodesics
Rhiannon Dougall, Richard Sharp
Let be a (non-elementary) convex co-compact group of isometries of a pinched Hadamard manifold . We show that a normal subgroup has critical exponent equal to the crit…