Scaling limit of the subdiffusive random walk on a Galton–Watson tree in random environment

A subdiffusive behaviour of recurrent random walk in random environment on a regular tree

We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk (Xn) in random environment on a regular tree, which is closely related to Mandelbrot [13]’s multiplicative cascade. We prove, under some general assumptions up...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Scaling Limit of Loop-erased Random Walk

The loop-erased random walk (LERW) was first studied in 1980 by Lawler as an attempt to analyze self-avoiding walk (SAW) which provides a model for the growth of a linear polymer in a good solvent. The self-avoiding walk is simply a path on a lattice that does not visit the same site more than once. Proving things about the collection of all such paths is a formidable challenge to rigorous math...

Scaling limit of simple random walk on supercritical percolation clusters

Scaling Limit of Loop Erased Random Walk — a Naive Approach

We give an alternative proof of the existence of the scaling limit of loop-erased random walk which does not use Löwner’s differential equation.