374 citations · 1.8k across the 64 of their papers we have counts for
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On the separation profile of infinite graphs
Itai Benjamini, Oded Schramm, Adam Timar
Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-kn…
Lack of Sphere Packing of Graphs via Non-Linear Potential Theory
Itai Benjamini, Oded Schramm
It is shown that there is no quasi-sphere packing of the lattice grid Z^{d+1} or a co-compact hyperbolic lattice of H^{d+1} or the 3-regular tree \times Z, in R^d, for all d. A sim…
Pinched exponential volume growth implies an infinite dimensional isoperimetric inequality
Itai Benjamini, Oded Schramm
Let be a graph which satisfies , for some constants , every vertex and every radius . We prove that this implies the isoperimet…
Average kissing numbers for non-congruent sphere packings
Greg Kuperberg, Oded Schramm
The Koebe circle packing theorem states that every finite planar graph can be realized as the nerve of a packing of (non-congruent) circles in R^3. We investigate the average kissi…