# Large Deviations of the Free Energy in the O’Connell–Yor Polymer

@article{Janjigian2014LargeDO, title={Large Deviations of the Free Energy in the O’Connell–Yor Polymer}, author={Christopher Janjigian}, journal={Journal of Statistical Physics}, year={2014}, volume={160}, pages={1054-1080} }

We investigate large deviations of the free energy in the O’Connell–Yor polymer through a variational representation of the positive real moment Lyapunov exponents of the associated parabolic Anderson model. Our methods yield an exact formula for all real moment Lyapunov exponents of the parabolic Anderson model and a dual representation of the large deviation rate function with normalization $$n$$n for the free energy.

## 13 Citations

### Determinantal Structures in the O’Connell-Yor Directed Random Polymer Model

- Mathematics
- 2015

We study the semi-discrete directed random polymer model introduced by O’Connell and Yor. We obtain a representation for the moment generating function of the polymer partition function in terms of a…

### Central moments of the free energy of the stationary O’Connell–Yor polymer

- MathematicsThe Annals of Applied Probability
- 2022

Seppäläinen and Valkó showed in [20] that for a suitable choice of parameters, the variance growth of the free energy of the stationary O’Connell-Yor polymer is governed by the exponent 2/3,…

### Concentration for integrable directed polymer models

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was…

### Central moments of the free energy of the O'Connell-Yor polymer

- Mathematics
- 2020

In this paper, we estimate the central moments of the stationary semi-discrete polymer in a Brownian environment, also known as the O'Connell-Yor polymer. From previous work of Seppalainen and Valko…

### Tail bounds for the O'Connell-Yor polymer

- Materials Science
- 2022

Abstract: We derive upper and lower bounds for the upper and lower tails of the O’ConnellYor polymer of the correct order of magnitude via probabilistic and geometric techniques in the moderate…

### Large deviations for some corner growth models with inhomogeneity

- Mathematics
- 2015

We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our main interest is in the quenched and annealed…

### Time evolution of the Kardar-Parisi-Zhang equation

- Mathematics
- 2020

The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The…

### A Large deviation principle for last passage times in an asymmetric Bernoulli potential

- Mathematics
- 2018

We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version…

### KPZ equation tails for general initial data

- Mathematics, Computer ScienceElectronic Journal of Probability
- 2020

The upper and lower tail probabilities for the centered and scaled one-point distribution of the Cole-Hopf solution of the KPZ equation when started with initial data drawn from a very general class are considered.

### Upper tail large deviations in Brownian directed percolation

- MathematicsElectronic Communications in Probability
- 2019

This paper presents a new, short proof of the computation of the upper tail large deviation rate function for the Brownian directed percolation model. Through a distributional equivalence between the…

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