11 papers · 1 filter
On the -rigidity phase transition in random graphs
Yuval Peled
We study generic -dimensional rigidity in sparse random graphs. Our main result is that for every , the Erdős--Rényi random graph undergoes a -rigidi…
The typical algebraic shifting of a surface
Denys Bulavka, Eran Nevo, Yuval Peled
We initiate a statistical study of Kalai's exterior algebraic shifting, focusing on concentration phenomena for random triangulations of a fixed space. First, for a uniform -ver…
When does a tree activate the random graph?
Asaf Cohen Antonir, Yuval Peled, Asaf Shapira +2
Let and be two graphs. A spanning subgraph of is called weakly -saturated if one can add to the edges of in some order, so that whenever a ne…
On the -volume rigidity of a simplicial complex in
Alan Lew, Eran Nevo, Yuval Peled +1
We define a generic rigidity matroid for -volumes of a simplicial complex in , and prove that for it has the same rank as the classical generic…
On the Rigidity of Random Graphs in high-dimensional spaces
Yuval Peled, Niv Peleg
We study the maximum dimension for which an Erdős-Rényi random graph is -rigid. Our main results reveal two different regimes of rigidity in separat…
Rigidity expander graphs
Alan Lew, Eran Nevo, Yuval Peled +1
Jordán and Tanigawa recently introduced the -dimensional algebraic connectivity of a graph . This is a quantitative measure of the -dimensional rigidity of wh…