Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework

Hans Chaumont; Christian Noack

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arXiv · 1711.08432

Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework

Hans Chaumont·Christian Noack

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Abstract

We develop a Mellin transform framework which allows us to simultaneously analyze the four known exactly solvable 1+1 dimensional lattice polymer models: the log-gamma, strict-weak, beta, and inverse-beta models. Using this framework we prove the conjectured fluctuation exponents of the free energy and the polymer path for the stationary point-to-point versions of these four models. The fluctuation exponent for the polymer path was previously unproved for the strict-weak, beta, and inverse-beta models.

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Hans Chaumont, Christian Noack. 2017-11-22. Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework. https://arxiv.org/abs/1711.08432

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