9 citations · 65 across the 21 of their papers we have counts for
5 papers · 1 filter
An isoperimetric constant for signed graphs
Antoine Gournay
A sign is introduced in the usual Laplacian on graphs and the corresponding analogue of the isoperimetric constant for this Laplacian is presented, i.e. a geometric quantity which…
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…