期刊
ANNALS OF PROBABILITY
卷 40, 期 1, 页码 19-73出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOP617
关键词
Scaling exponent; directed polymer; random environment; superdiffusivity; Burke's theorem; partition function
资金
- NSF [DMS-07-01091, DMS-10-03651]
- Wisconsin Alumni Research Foundation
- Division Of Mathematical Sciences [1003651] Funding Source: National Science Foundation
We study a (1 + 1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with exponential or geometric weights is special among growth models, namely, both permit explicit calculations. With appropriate boundary conditions, the polymer with log-gamma weights satisfies an analogue of Burke's theorem for queues. Building on this, we prove the conjectured values for the fluctuation exponents of the free energy and the polymer path, in the case where the boundary conditions are present and both endpoints of the polymer path are fixed. For the polymer without boundary conditions and with either fixed or free endpoint, we get the expected upper bounds on the exponents.
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