# Large deviations for some corner growth models with inhomogeneity

@article{Emrah2015LargeDF, title={Large deviations for some corner growth models with inhomogeneity}, author={Elnur Emrah and Christopher Janjigian}, journal={arXiv: Probability}, year={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 large deviation properties of the last passage times. We derive variational representations of the rate functions for right tail large deviations. The quenched rate function can be computed explicitly for certain choices of the parameter distributions. We present a mechanism for rate n left tail…

## 13 Citations

### Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model

- Mathematics
- 2019

We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exponentials are given…

### Limit shapes for inhomogeneous corner growth models with exponential and geometric weights

- Mathematics
- 2016

We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ at site $(i, j)$,…

### Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment

- Mathematics, Computer Science
- 2016

The rate functions of the level-3 averaged and quenched large deviation principles from the point of view of the particle are studied and the minimizers of thelevel-3 to level-1 contractions in both settings are identified.

### Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models

- Mathematics
- 2016

We study a class of corner growth models in which the weights are either all exponentially or all geometrically distributed. The parameter of the distribution at site $(i, j)$ is $a_i+b_j$ in the…

### Right-tail moderate deviations in the exponential last-passage percolation.

- Mathematics
- 2020

We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on the last-passage…

### Last passage percolation in an exponential environment with discontinuous rates

- Mathematics
- 2018

We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a…

### 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…

### Large Deviations for Brownian Particle Systems with Killing

- Mathematics
- 2016

Particle approximations for certain nonlinear and nonlocal reaction–diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d.…

### 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…

### Fluctuations of the corner growth model with geometric weights

- Mathematics
- 2016

The corner growth model describes a random region growing over time in the first quadrant of the plane, and is closely related to totally asymmetric simple exclusion process (TASEP), queues in series…

## References

SHOWING 1-10 OF 37 REFERENCES

### Limit shapes for inhomogeneous corner growth models with exponential and geometric weights

- Mathematics
- 2016

We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ at site $(i, j)$,…

### Large deviation rate functions for the partition function in a log-gamma distributed random potential

- Mathematics
- 2011

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the…

### Fluctuations in the Composite Regime of a Disordered Growth Model

- Mathematics
- 2002

Abstract: We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one-dimensional integer lattice and grows in…

### A Course on Large Deviations With an Introduction to Gibbs Measures

- Mathematics
- 2015

Large deviations: General theory and i.i.d. processes Introductory discussion The large deviation principle Large deviations and asymptotics of integrals Convex analysis in large deviation theory…

### Large deviations for increasing sequences on the plane

- Mathematics
- 1998

Abstract. We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among Poisson points on the plane. The rate function for lower tail…

### Quenched, annealed and functional large deviations for one-dimensional random walk in random environment

- Mathematics
- 2000

Suppose that the integers are assigned random variables {ωi} (taking values in the unit interval), which serve as an environment. This environment defines a random walk {Xn} (called a RWRE) which,…

### Scaling for a one-dimensional directed polymer with boundary conditions

- Mathematics
- 2009

We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the…

### Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

- Mathematics
- 2000

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function ht(x) with corner initialization. We prove, with one exception, that the…

### A growth model in a random environment

- Mathematics
- 2000

We consider a model of interface growth in two dimensions, given by a height
function on the sites of the one--dimensional integer lattice. According to the discrete
time update rule, the height…

### Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder

- Mathematics
- 1999

We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. We…