11 citations · 23 across the 5 of their papers we have counts for
5 papers · 1 filter
Limiting distributions for RWCRE in the sub-ballistic regime and in the critical Gaussian regime
Conrado da Costa, Jonathon Peterson, Yongjia Xie
Random Walks in Cooling Random Environments (RWCRE) is a model of random walks in dynamic random environments where the environment is frozen between a fixed sequence of times (cal…
Variable speed symmetric random walk driven by symmetric exclusion
Otávio Menezes, Jonathon Peterson, Yongjia Xie
We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of…
Functional Weak Limit of Random Walks in Cooling Random Environment
Yongjia Xie
We prove an annealed weak limit of the trajectory of the random walks in cooling random environment (RWCRE) under both slow (polynomial) and fast (exponential) cooling. We identify…
On the Law of Large Numbers for the empirical measure process of Generalized Dyson Brownian motion
Songzi Li, Xiang-Dong Li, Yong-Xiao Xie
We study the generalized Dyson Brownian motion (GDBM) of an interacting -particle system with logarithmic Coulomb interaction and general potential . Under reasonable conditi…
Generalized Dyson Brownian motion, McKean-Vlasov equation and eigenvalues of random matrices
Songzi Li, Xiang-Dong Li, Yong-Xiao Xie
Using Itô's calculus and the mass optimal transportation theory, we study the generalized Dyson Brownian motion (GDBM) and the associated McKean-Vlasov evolution equation with an e…