Vertex-Reinforced Random Walk
| dc.creator | Pemantle, Robin | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:02Z | |
| dc.date.available | 2026-07-07T05:07:02Z | |
| dc.description | This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1,...,d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a priori likelihood matrix, R, which is real, symmetric and nonnegative. Let S_i(n) keep track of the number of visits to state i up to time n, and form the fractional occupation vector, V(n), where v_i(n)=S_i(n)/(sum_{j=1}^d S_j(n)). It is shown that V(n) converges to a set of critical points for the quadratic form H with matrix R, and that under nondegeneracy conditions on R, there is a finite set of points such that with probability one, V(n)->p for some p in the set. There may be more than one p in this set for which P(V(n)->p)>0. On the other hand P(V(n)->p)=0 whenever p fails in a strong enough sense to be maximum for H. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404041 | |
| dc.identifier | http://arxiv.org/abs/math/0404041 | |
| dc.identifier | Prob. Theor. and Rel. Fields, 92, 117 - 136 (1990) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70698 | |
| dc.subject | Probability | |
| dc.title | Vertex-Reinforced Random Walk | |
| dc.type | text |