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Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

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Abstract

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.

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Acknowledgements

YB gratefully acknowledges partial support from NSF through Grant DMS-1460595.

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  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY, 10012, USA

    Yuri Bakhtin & Liying Li

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  1. Yuri Bakhtin
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  2. Liying Li
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Correspondence to Yuri Bakhtin.

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Bakhtin, Y., Li, L. Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation. J Stat Phys 172, 1358–1397 (2018). https://doi.org/10.1007/s10955-018-2104-z

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  • DOI: https://doi.org/10.1007/s10955-018-2104-z

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