Niv Peleg

On the rigidity of random graphs in high-dimensional spaces

We study the maximum dimension $d=d(n,p)$ for which an Erdős-Rényi $G(n,p)$ random graph is $d$-rigid. Our main results reveal two different regimes of rigidity in $G(n,p)$ separated at $p_c=C_*\log n/n,~C_*=2/(1-\log 2)$ -- the point where the graph's minimum degree exceeds half...