# The KPZ universality class and related topics

@article{Saenz2020TheKU, title={The KPZ universality class and related topics}, author={Axel Saenz}, journal={Analytic Trends in Mathematical Physics}, year={2020} }

These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random growth processes in $1+1$ dimensions. We describe some of the characteristic properties of the KPZ universality class such as scaling exponents and limiting statistics. In particular, we aim to extract the characteristic properties of the KPZ…

## 5 Citations

Spectral gaps of open TASEP in the maximal current phase

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We study spectral gaps of the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries in the maximal current phase. Earlier results for the model with periodic…

Riemann surface crossover for the spectral gaps of open TASEP

- Mathematics
- 2021

We consider the totally asymmetric simple exclusion process (TASEP) with open boundaries, at the edge of the maximal current (MC) phase. Using analytic continuations from the known stationary…

Cluster dynamics in the open-boundary heterogeneous ASEPs coupled with interacting energies

- PhysicsThe European Physical Journal Plus
- 2020

Cluster dynamics possess the promising studies in statistical physics and complexity science. While proposing physical models, applying analytical methods and exploring macroscopic properties and…

Riemann surface for TASEP with periodic boundaries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

The Bethe ansatz solution of periodic TASEP is formulated in terms of a ramified covering from a Riemann surface to the sphere. The joint probability distribution of height fluctuations at n distinct…

Riemann surfaces for KPZ with periodic boundaries

- MathematicsSciPost Physics
- 2020

The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to one-dimensional KPZ universality in finite volume.…

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