Gaussian fluctuations of replica overlap in directed polymers

@article{Gu2022GaussianFO,
  title={Gaussian fluctuations of replica overlap in directed polymers},
  author={Yu Gu and Tomasz Komorowski},
  journal={Electronic Communications in Probability},
  year={2022}
}
  • Yu Gu, T. Komorowski
  • Published 1 January 2022
  • Mathematics
  • Electronic Communications in Probability
. In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a superconcentration result for the KPZ equation driven by a spatially mollified noise, which is inspired by the recent work of Chatterjee [14]. 

References

SHOWING 1-10 OF 37 REFERENCES

INFLUENCE OF SPATIAL CORRELATION FOR DIRECTED POLYMERS

In this paper, we study a model of a Brownian polymer in ℝ + x ℝ d , introduced by Rovira and Tindel [J. Funct. Anal. 222 (2005) 178-201]. Our investigation focuses mainly on the effect of strong

Localization Transition for Polymers in Poissonian Medium

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

Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature

Strong localization and macroscopic atoms for directed polymers

In this article, we derive strong localization results for directed polymers in random environment. We show that at “low temperature” the polymer measure is asymptotically concentrated at a few

Directed polymers in a random environment: path localization and strong disorder

We consider directed polymers in random environment. Under some mild assumptions on the environment, we prove here: (i) equivalence between the decay rate of the partition function and some natural

Localization in Gaussian disordered systems at low temperature

TLDR
A version of "complete" path localization for directed polymers that is not available even for exactly solvable models and a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities are obtained.

The endpoint distribution of directed polymers

Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we

Sublinear Variance for Directed Last-Passage Percolation

A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with

Scaling for a one-dimensional directed polymer with boundary conditions

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