# One-point asymptotics for half-flat ASEP

@inproceedings{Dimitrov2022OnepointAF, title={One-point asymptotics for half-flat ASEP}, author={Evgeni Dimitrov and Anushka Murthy}, year={2022} }

. We consider the asymmetric simple exclusion process (ASEP) with half-ﬂat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the Airy 2 → 1 process, introduced by Borodin-Ferrari-Sasamoto in (Commun. Pure Appl. Math., 61, 1603-1629, 2008). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab., 26, 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-ﬂat ASEP…

## References

SHOWING 1-10 OF 32 REFERENCES

### KPZ and Airy limits of Hall-Littlewood random plane partitions

- Mathematics
- 2016

In this paper we consider a probability distribution on plane partitions, which arises as a one-parameter generalization of the q^{volume} measure. This generalization is closely related to the…

### Convergence of exclusion processes and the KPZ equation to the KPZ fixed point

- Mathematics
- 2020

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point,…

### Continuum Statistics of the Airy2 Process

- Mathematics
- 2013

We develop an exact determinantal formula for the probability that the Airy_2 process is bounded by a function g on a finite interval. As an application, we provide a direct proof that…

### The KPZ fixed point

- MathematicsActa Mathematica
- 2021

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process with arbitrary initial condition. The…

### From duality to determinants for q-TASEP and ASEP

- Mathematics
- 2014

We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).…

### Two-point convergence of the stochastic six-vertex model to the Airy process

- Mathematics
- 2020

In this paper we consider the stochastic six-vertex model in the quadrant started with step initial data. After a long time $T$, it is known that the one-point height function fluctuations are of…

### Transition between Airy1 and Airy2 processes and TASEP fluctuations

- Computer Science
- 2007

In this paper the totally asymmetric simple exclusion process is considered, a model in the KPZ universality class, and its one‐point distribution is a new interpolation between GOE and GUE edge distributions.

### Discrete Polynuclear Growth and Determinantal Processes

- Mathematics
- 2003

AbstractWe consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn.…

### 21pYO-3 Spatial correlations of the 1D KPZ surface on a flat substrate

- Mathematics
- 2005

We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm…

### Scale Invariance of the PNG Droplet and the Airy Process

- Mathematics
- 2001

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy…