30 citations · 38 across the 4 of their papers we have counts for
6 papers
Limit shapes for Gibbs partitions of sets
Ibrahim Fatkullin, Jianfei Xue
This study extends a prior investigation of limit shapes for partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes…
On Hydrodynamic Limits of Young Diagrams
Ibrahim Fatkullin, Sunder Sethuraman, Jianfei Xue
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of…
Limit shapes for Gibbs ensembles of partitions
Ibrahim Fatkullin, Valeriy Slastikov
We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to in…
Coalescing particle systems and applications to nonlinear Fokker-Planck equations
Gleb Zhelezov, Ibrahim Fatkullin
We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bes…
Diffusive transport in two-dimensional nematics
Ibrahim Fatkullin, Valeriy Slastikov
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolu…
A study of blow-ups in the Keller-Segel model of chemotaxis
Ibrahim Fatkullin
We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solu…