A class of families of Markov chains defined on the vertices of the n-dimensional hypercube, Ω n ={0,1} n , is studied. The single-step transition probabilities P n,ij , with i,j∈Ω n , are given by Pn,ij=\frac(1-a)dij(2-a)nPnij=(2−)n(1−)dij, where α∈(0,1) and d ij is the Hamming distance between i and j. This corresponds to flip independently each component of the vertex with probability \frac1-a2-a2−1−. The m-step transition matrix Pn,ijmPmnij is explicitly computed in a close form. The class is proved to exhibit cutoff. A model-independent result about the vanishing of the first m terms of the expansion in α of Pn,ijmPmnij is also proved.
Scoppola, B. (2011). Exact Solution for a Class of Random Walk on the Hypercube. JOURNAL OF STATISTICAL PHYSICS, 143(3), 413-419.
Tipologia: | Articolo su rivista |
Citazione: | Scoppola, B. (2011). Exact Solution for a Class of Random Walk on the Hypercube. JOURNAL OF STATISTICAL PHYSICS, 143(3), 413-419. |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10955-011-0194-y |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2011 |
Titolo: | Exact Solution for a Class of Random Walk on the Hypercube |
Autori: | |
Autori: | Scoppola, B |
Appare nelle tipologie: | 01 - Articolo su rivista |