Loop-erased random walk is a model for a random simple (i.e. non-selfintersecting) path created by taking a random walk and, whenever it hits itself, deleting the resulting loop and continuing. We will explain why this model is interesting and why scaling limits are interesting, and then go on to describe the proof (that the limit exists), as time will permit.

The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this “deterministic random walk” covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several impo...

Exploiting the coherent medium approximation, I investigate a random walk on objects distributed randomly in continuous space when jump rate depends distance between two adjacent objects. In one dimension, it is shown that decays exponentially long limit, non-diffusive to diffusive transition occurs as density of sites increased. three dimensions, exists has super Gaussian decay.

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-ofthe-art word2vec model to embed a graph in Euclidean space via random walks on the nodes of the graph. In VEC-NBT, we modify the original algorithm to use a non-b...

A random walk model of mobile cellular network is essential for analysis of roaming and handover of the network. Since handover call arrival is an important parameter of mobile cellular network traffic hence efficiency of a random walk model play important role in both network planning and channel management. This paper proposes a new random walk model of hexagonal cell cluster, exclusively don...