9 citations · 65 across the 21 of their papers we have counts for
23 papers
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…
Balancing non-rectangular tables
Antoine Gournay
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act…
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…
On Critical nets in
Antoine Gournay, Yashar Memarian
Critical nets in (sometimes called geodesic nets) are embedded graph with the property that their embedding is a critical point of the total (edge) length functional…
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…
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…
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…
Further properties of dimension
Antoine Gournay
This article establishes more properties of the dimension introduced in a previous article. Given an amenable group acting by translation on , this is just…
Time delay and Calabi invariant in classical scattering theory
Antoine Gournay, Rafael Tiedra de Aldecoa
We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H_0,H) on a symplectic mani…
A formula relating localisation observables to the variation of energy in Hamiltonian dynamics
Antoine Gournay, Rafael Tiedra de Aldecoa
We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi…
On a Hölder covariant version of mean dimension
Antoine Gournay
Let G be a infinite countable group which acts naturally on l^p(G). We introduce a modification of mean dimension which is an obstruction for l^p(G) and l^q(G) to be Hölder conjuga…
Complex surfaces and interpolation on pseudo-holomorphic cylinders
Antoine Gournay
Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for…
A Runge approximation theorem for pseudo-holomorphic maps
Antoine Gournay
The Runge approximation theorem for holomorphic maps (U -> C) is a fundamental result in complex analysis. The aim of this article is to prove such a result for (pseudo-)holomorphi…
A dynamical approach to von Neumann dimension
Antoine Gournay
Let G be an amenable group and V be a finite dimensional vector space. Gromov pointed out that the von Neumann dimension of linear subspaces of l^2(G;V) (with respect to G) can be…
Width of l^p balls
Antoine Gournay
We say a map f:X \to Y is an ε-embedding if it is continuous and the diameter of the fibres is less than ε. This type of maps is used in the notion of Urysohn width (sometimes refe…