9 citations · 65 across the 21 of their papers we have counts for
12 papers · 1 filter
Cuts, flows and gradient conditions on harmonic functions
Antoine Gournay
Reduced cohomology motivates to look at harmonic functions which satisfy certain gradient conditions. If is a direct product of two infinite groups or a (FC-central)-by-cyclic…
Separation profiles, isoperimetry, growth and compression
Corentin Le Coz, Antoine Gournay
We give lower and upper bounds for the separation profile (introduced by Benjamini, Schramm & Timár) for various graphs using the isoperimetric profile, growth and Hilbertian compr…
Mixing, malnormal subgroups and cohomology in degree one
Antoine Gournay
The aim of the current paper is to explore the implications on the group of the non-vanishing of the cohomology in degree one of one of its representation , given some mixin…
Connectedness of spheres in Cayley graphs
Jérémie Brieussel, Antoine Gournay
We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded f…
Harmonic functions with finite -energy on lamplighter graphs are constant
Antoine Gournay
The aim of this note is to show that lamplighter graphs where the space graph is infinite and at most two-ended and the lamp graph is at most two-ended do not admit harmonic functi…
Functions conditionally of negative type on groups acting on regular trees
Antoine Gournay, Pierre-Nicolas Jolissaint
Let be the -regular tree and let be a group of automorphisms acting transitively on the vertices and on the boundary of . We give…
The Liouville property and Hilbertian compression
Antoine Gournay
Lower bound on the equivariant Hilbertian compression exponent are obtained using random walks. More precisely, if the probability of return of the simple random walk is $\succ…
Amenability criterions and critical probabilities in percolation
Antoine Gournay
A new proof of a Theorem of Nagnibeda and Pak on critical probabilities is given. The distinctive feature is to use a criterion of Folner which has been largely (and inexplicably)…
Absence of non-constant harmonic functions with -gradient in some semi-direct products
Antoine Gournay
To obtain groups with bounded harmonic functions (which are not hyperbolic), one of the most frequent way is to look at some semi-direct products (\eg lamplighter groups). The aim…
A remark on the connectedness of spheres in Cayley graphs
Antoine Gournay
The aim of this small note is to prove an elementary yet useful properties of finitely presented groups. Let G be a finitely generated group with one end. Fix a (finite) generating…
Boundary values, random walks and -cohomology in degree one
Antoine Gournay
The vanishing of reduced -cohomology for amenable groups can be traced to the work of Cheeger & Gromov. The subject matter here is reduced -cohomology for $p \in ]1…
Vanishing of -cohomology and transportation cost
Antoine Gournay
In this paper, it is shown that the reduced -cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for w…