Localization transition for polymers in Poissonian medium.(English)Zbl 1276.82066
Summary: We study a model of directed polymers in random environment in dimension \(1 + d\), given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively, the intensity parameter \(\nu \) of the Poisson field and temperature inverse \(\beta \). We obtain (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large \(\nu \beta ^{2}\) and bounded \(\beta \).
MSC:
| 82D60 | Statistical mechanics of polymers |
| 60J65 | Brownian motion |
| 60K37 | Processes in random environments |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
Cite
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