Scaling for a one-dimensional directed polymer with boundary conditions

By T. Seppalainen. 2009

213 citations recorded by the source corpus.

We study a 1 + 1-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights and both endpoints of the path fixed. 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 that the fluctuation exponents for the free energy and the polymer path have their conjectured values. For the polymer without boundary conditions and with either fixed or free endpoint we get the expected upper bounds on the exponents.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2930da37c682b708ca7bf353126037346581984c

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Introduction to KPZ (2011, background): “Results on ζ = 2/3 have recently been obtained in special models [11],[109].”
Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, result): “These results significantly expand upon the previous proved results for positive temperature polymer models [5, 16, 25, 57, 58].”