Contest based on a directed polymer in a random medium
| dc.creator | Sire, Clément | |
| dc.date | 2008-07-24 | |
| dc.date | 2008-12-06 | |
| dc.date.accessioned | 2026-07-07T12:09:41Z | |
| dc.date.available | 2026-07-07T12:09:41Z | |
| dc.description | We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score, and minimize opponent's return. For a game of length $n$, we find that the probability distribution of the final score $S_n$ develops a traveling wave form, ${\rm Prob}(S_n=m)=f(m-v n)$, with the wave profile $f(z)$ unusually decaying as a double exponential for large positive and negative $z$. In addition, as the only parameter in the game is varied, we find a transition where one player is able to get his maximum theoretical score. By extending this model, we suggest that the front velocity $v$ is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially, and for which standard traveling wave theory applies. | |
| dc.identifier | https://arxiv.org/abs/0807.3779 | |
| dc.identifier | http://arxiv.org/abs/0807.3779 | |
| dc.identifier | Phys. Rev. E 78, 061106 (2008) | |
| dc.identifier | doi:10.1103/PhysRevE.78.061106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209706 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Contest based on a directed polymer in a random medium | |
| dc.type | text |