87 citations · 243 across the 20 of their papers we have counts for
5 papers · 1 filter
Explosive percolation on scale-free multifractal weighted planar stochastic lattice
M. K. Hassan, M. M. Rahman
In this article, we investigate explosive bond percolation (EBP) with product rule, formally known as Achlioptas process, on a scale-free multifractal weighted planar stochastic la…
Brownian motion as limit of the interchange process
Mustazee Rahman, Balint Virag
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure o…
Geometry of Permutation Limits
Mustazee Rahman, Balint Virag, Mate Vizer
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting n…
A lower bound on the spectrum of unimodular networks
Mustazee Rahman
Unimodular networks are a generalization of finite graphs in a stochastic sense. We prove a lower bound to the spectral radius of the adjacency operator and of the Markov operator…
Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice
M. K. Hassan, M. M. Rahman
In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network.…