On Random Graph Homomorphisms into Z

On Random Graph Homomorphisms into Z

Given a bipartite connected finite graph G=(V, E) and a vertex v0∈V, we consider a uniform probability measure on the set of graph homomorphisms f: V→Z satisfying f(v0)=0. This measure can be viewed as a Gindexed random walk on Z, generalizing both the usual time-indexed random walk and tree-indexed random walk. Several general inequalities for the G-indexed random walk are derived, including a...

Upper bounds on the height difference of the Gaussian random field and the range of random graph homomorphisms into Z

Bounds on the range of random graph homomorphism into Z, and the maximal height difference of the Gaussian random field, are presented.

Upper Bounds on the Height Diierence of the Gaussian Random Field and the Range of Random Graph Homomorphisms into Z

Bounds on the range of random graph homomorphism into Z, and the maximal height diierence of the Gaussian random eld, are presented.

Graph homomorphisms through random walks

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff– Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which...

Random Walks and Graph Homomorphisms