𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Natural spanning trees of Zd are recurrent

✍ Scribed by Peter Gerl

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
169 KB
Volume
61
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

We show that the simple random walk on the natural spanning tree of 7/d is recurrent for every d ( = 1, 2, 3,...) and determine the asymptotic behaviour of the probability of returning to the origin in n steps (n--, 0o). This is in contrast to a result of Polya [6]: Z d is recurrent for d = 1, 2 and transient for d t> 3.

πŸ“œ SIMILAR VOLUMES

On mean recurrence times of Markov chain
On mean recurrence times of Markov chains and spanning tree invariants
✍ Ricardo GΓ³mez πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 141 KB

We show that the mean recurrence times of (countable state) irreducible and positively recurrent Markov chains are the spanning tree invariants of the first return loop systems. Then, by the Perron-Frobenius Theorem, the spanning tree invariants of the first return loop systems of a finite state Mar