Contest based on a directed polymer in a random medium

dc.creatorSire, Clément
dc.date2008-07-24
dc.date2008-12-06
dc.date.accessioned2026-07-07T12:09:41Z
dc.date.available2026-07-07T12:09:41Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/0807.3779
dc.identifierhttp://arxiv.org/abs/0807.3779
dc.identifierPhys. Rev. E 78, 061106 (2008)
dc.identifierdoi:10.1103/PhysRevE.78.061106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209706
dc.subjectStatistical Mechanics
dc.titleContest based on a directed polymer in a random medium
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