منابع مشابه
Processes on Unimodular Random Networks
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning random walks, percolation, spanning forests, and amenability from the known context of unimodular quasi-transitive graphs to the more general context of unimodu...
متن کاملErrata to Processes on Unimodular Random Networks
The statement in the introduction, “Unimodularity of a probability measure μ on rooted graphs is equivalent to the property that a reversible stationary distribution for this chain is given by the root-degree biasing of μ . . . ”, is incorrect. Unimodularity implies this reversibility, but is not implied by it. There is a similar loss of precision at the beginning of Section 4. The correct stat...
متن کاملDynamics on Unimodular Random Graphs
This paper is centered on covariant dynamics on random graphs and random networks (marked graphs), which can be described as rules to navigate the vertices that are preserved by graph/network isomorphisms. Such dynamics are referred to as vertex-shifts here. Unimodular random networks can be heuristically described as networks seen from a vertex chosen uniformly at random, both in the finite an...
متن کاملUnimodular random trees
We consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root in an invariant percolation on a regular tree. We use this to give a new proof that URTs are sofic, a result of Elek. We show that ends of invariant forests in the hyperbolic plane converge to ideal boundary points. We...
متن کاملRandom walk and trapping processes on scale-free networks.
In this work I investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. I perform extensive simulations for the calculation of the mean squared displacement, the network coverage, and the survival probability on a network with a concentration c of static traps. It is shown that the random walkers remain close to their origin, but cover a large ...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2007
ISSN: 1083-6489
DOI: 10.1214/ejp.v12-463