# Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models

## TL;DR

This paper investigates the universal fluctuation behaviors in crossing KPZ interfaces with different initial conditions, revealing a phase transition in fluctuation distributions governed by a control parameter.

## Contribution

It introduces a phase diagram for crossing KPZ interfaces and identifies a transition between Tracy-Widom distributions and Gaussian behavior at a critical point p=0.5.

## Key findings

- Distribution converges to GOE TW for p<0.5
- Distribution converges to GUE TW for p>0.5
- At p=0.5, Gaussian statistics emerge

## Abstract

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom (TW) distribution for p<0.5, and to the Gaussian unitary ensemble TW distribution for p>0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.