87 citations · 243 across the 20 of their papers we have counts for
Showing 2014 · math.PRShow all
3 papers · 2 filters
math.PR2014★ 12 cited
Factor of iid percolation on trees
Mustazee Rahman
We study invariant percolation processes on the d-regular tree that are obtained as a factor of an iid process. We show that the density of any factor of iid site percolation proce…
math.PR2014★ 2 cited
Percolation with small clusters on random graphs
Mustazee Rahman
Consider the problem of determining the maximal induced subgraph in a random -regular graph such that its components remain bounded as the size of the graph becomes arbitrarily…
math.PR2014★ 87 cited
Local algorithms for independent sets are half-optimal
Mustazee Rahman, Balint Virag
We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d tends to infinity. This matches the lower bound…